(3x+4)(x-6)=9x+12

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Solution for (3x+4)(x-6)=9x+12 equation: 


Simplifying
(3x + 4)(x + -6) = 9x + 12

Reorder the terms:
(4 + 3x)(x + -6) = 9x + 12

Reorder the terms:
(4 + 3x)(-6 + x) = 9x + 12

Multiply (4 + 3x) * (-6 + x)
(4(-6 + x) + 3x * (-6 + x)) = 9x + 12
((-6 * 4 + x * 4) + 3x * (-6 + x)) = 9x + 12
((-24 + 4x) + 3x * (-6 + x)) = 9x + 12
(-24 + 4x + (-6 * 3x + x * 3x)) = 9x + 12
(-24 + 4x + (-18x + 3x2)) = 9x + 12

Combine like terms: 4x + -18x = -14x
(-24 + -14x + 3x2) = 9x + 12

Reorder the terms:
-24 + -14x + 3x2 = 12 + 9x

Solving
-24 + -14x + 3x2 = 12 + 9x

Solving for variable 'x'.

Reorder the terms:
-24 + -12 + -14x + -9x + 3x2 = 12 + 9x + -12 + -9x

Combine like terms: -24 + -12 = -36
-36 + -14x + -9x + 3x2 = 12 + 9x + -12 + -9x

Combine like terms: -14x + -9x = -23x
-36 + -23x + 3x2 = 12 + 9x + -12 + -9x

Reorder the terms:
-36 + -23x + 3x2 = 12 + -12 + 9x + -9x

Combine like terms: 12 + -12 = 0
-36 + -23x + 3x2 = 0 + 9x + -9x
-36 + -23x + 3x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-36 + -23x + 3x2 = 0

Factor a trinomial.
(-4 + -3x)(9 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-1.333333333, 9}

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