352=9x^2+15x+52

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Solution for 352=9x^2+15x+52 equation: 


Simplifying
352 = 9x2 + 15x + 52

Reorder the terms:
352 = 52 + 15x + 9x2

Solving
352 = 52 + 15x + 9x2

Solving for variable 'x'.

Combine like terms: 352 + -52 = 300
300 + -15x + -9x2 = 52 + 15x + 9x2 + -52 + -15x + -9x2

Reorder the terms:
300 + -15x + -9x2 = 52 + -52 + 15x + -15x + 9x2 + -9x2

Combine like terms: 52 + -52 = 0
300 + -15x + -9x2 = 0 + 15x + -15x + 9x2 + -9x2
300 + -15x + -9x2 = 15x + -15x + 9x2 + -9x2

Combine like terms: 15x + -15x = 0
300 + -15x + -9x2 = 0 + 9x2 + -9x2
300 + -15x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
300 + -15x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(100 + -5x + -3x2) = 0

Factor a trinomial.
3((5 + -1x)(20 + 3x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(20 + 3x)' equal to zero and attempt to solve:

Simplifying
20 + 3x = 0

Solving
20 + 3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-20' to each side of the equation.
20 + -20 + 3x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 3x = 0 + -20
3x = 0 + -20

Combine like terms: 0 + -20 = -20
3x = -20

Divide each side by '3'.
x = -6.666666667

Simplifying
x = -6.666666667
Solution
x = {5, -6.666666667}

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