(2x^2+12x)=(3x-9)

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Solution for (2x^2+12x)=(3x-9) equation: 


Simplifying
(2x2 + 12x) = (3x + -9)

Reorder the terms:
(12x + 2x2) = (3x + -9)

Remove parenthesis around (12x + 2x2)
12x + 2x2 = (3x + -9)

Reorder the terms:
12x + 2x2 = (-9 + 3x)

Remove parenthesis around (-9 + 3x)
12x + 2x2 = -9 + 3x

Solving
12x + 2x2 = -9 + 3x

Solving for variable 'x'.

Reorder the terms:
9 + 12x + -3x + 2x2 = -9 + 3x + 9 + -3x

Combine like terms: 12x + -3x = 9x
9 + 9x + 2x2 = -9 + 3x + 9 + -3x

Reorder the terms:
9 + 9x + 2x2 = -9 + 9 + 3x + -3x

Combine like terms: -9 + 9 = 0
9 + 9x + 2x2 = 0 + 3x + -3x
9 + 9x + 2x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
9 + 9x + 2x2 = 0

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


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}

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