(2x+3)(x-3)=8x+12

Solution for (2x+3)(x-3)=8x+12 equation:

Simplifying
(2x + 3)(x + -3) = 8x + 12

Reorder the terms:
(3 + 2x)(x + -3) = 8x + 12

Reorder the terms:
(3 + 2x)(-3 + x) = 8x + 12

Multiply (3 + 2x) * (-3 + x)
(3(-3 + x) + 2x * (-3 + x)) = 8x + 12
((-3 * 3 + x * 3) + 2x * (-3 + x)) = 8x + 12
((-9 + 3x) + 2x * (-3 + x)) = 8x + 12
(-9 + 3x + (-3 * 2x + x * 2x)) = 8x + 12
(-9 + 3x + (-6x + 2x2)) = 8x + 12

Combine like terms: 3x + -6x = -3x
(-9 + -3x + 2x2) = 8x + 12

Reorder the terms:
-9 + -3x + 2x2 = 12 + 8x

Solving
-9 + -3x + 2x2 = 12 + 8x

Solving for variable 'x'.

Reorder the terms:
-9 + -12 + -3x + -8x + 2x2 = 12 + 8x + -12 + -8x

Combine like terms: -9 + -12 = -21
-21 + -3x + -8x + 2x2 = 12 + 8x + -12 + -8x

Combine like terms: -3x + -8x = -11x
-21 + -11x + 2x2 = 12 + 8x + -12 + -8x

Reorder the terms:
-21 + -11x + 2x2 = 12 + -12 + 8x + -8x

Combine like terms: 12 + -12 = 0
-21 + -11x + 2x2 = 0 + 8x + -8x
-21 + -11x + 2x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-21 + -11x + 2x2 = 0

Factor a trinomial.
(-3 + -2x)(7 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-1.5, 7}