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

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

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

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

Reorder the terms:
12x + x2 = 12(-3 + 2x)
12x + x2 = (-3 * 12 + 2x * 12)
12x + x2 = (-36 + 24x)

Solving
12x + x2 = -36 + 24x

Solving for variable 'x'.

Reorder the terms:
36 + 12x + -24x + x2 = -36 + 24x + 36 + -24x

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

Reorder the terms:
36 + -12x + x2 = -36 + 36 + 24x + -24x

Combine like terms: -36 + 36 = 0
36 + -12x + x2 = 0 + 24x + -24x
36 + -12x + x2 = 24x + -24x

Combine like terms: 24x + -24x = 0
36 + -12x + x2 = 0

Factor a trinomial.
(6 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {6, 6}