# Solve for x 4sin(x)^2+4sin(x)-3=0

Solve for x 4sin(x)^2+4sin(x)-3=0
Factor the left side of the equation.
Let . Substitute for all occurrences of .
Factor by grouping.
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Factor out of .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
Replace all occurrences of with .
Replace the left side with the factored expression.
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to and solve.
Set the first factor equal to .
Add to both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Take the inverse sine of both sides of the equation to extract from inside the sine.
The exact value of is .
The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from to find the solution in the second quadrant.
Simplify .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Move to the left of .
Subtract from .
Find the period.
The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
The period of the function is so values will repeat every radians in both directions.
, for any integer
, for any integer
Set the next factor equal to and solve.
Set the next factor equal to .
Subtract from both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Move the negative in front of the fraction.
The range of sine is . Since does not fall in this range, there is no solution.
No solution
No solution
The final solution is all the values that make true.
, for any integer
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### Name

Name one billion nine hundred fifty-seven million nine hundred eighteen thousand three hundred ninety-two

### Interesting facts

• 1957918392 has 128 divisors, whose sum is 13052793600
• The reverse of 1957918392 is 2938197591
• Previous prime number is 3

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 54
• Digital Root 9

### Name

Name one hundred seventy-one million one hundred twenty-eight thousand nine hundred twenty-eight

### Interesting facts

• 171128928 has 256 divisors, whose sum is 1788604416
• The reverse of 171128928 is 829821171
• Previous prime number is 31

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 39
• Digital Root 3

### Name

Name three hundred sixty-five million seven hundred ninety-two thousand two hundred eighteen

### Interesting facts

• 365792218 has 32 divisors, whose sum is 631800000
• The reverse of 365792218 is 812297563
• Previous prime number is 449

### Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 43
• Digital Root 7