6-2x^2=9x+15

Solution for 6-2x^2=9x+15 equation:

Simplifying
6 + -2x2 = 9x + 15

Reorder the terms:
6 + -2x2 = 15 + 9x

Solving
6 + -2x2 = 15 + 9x

Solving for variable 'x'.

Reorder the terms:
6 + -15 + -9x + -2x2 = 15 + 9x + -15 + -9x

Combine like terms: 6 + -15 = -9
-9 + -9x + -2x2 = 15 + 9x + -15 + -9x

Reorder the terms:
-9 + -9x + -2x2 = 15 + -15 + 9x + -9x

Combine like terms: 15 + -15 = 0
-9 + -9x + -2x2 = 0 + 9x + -9x
-9 + -9x + -2x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-9 + -9x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(9 + 9x + 2x2) = 0

Factor a trinomial.
-1((3 + x)(3 + 2x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

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

Simplifying
3 + 2x = 0

Solving
3 + 2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {-3, -1.5}