2x(x-2)=x+12

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

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

Reorder the terms:
2x(-2 + x) = x + 12
(-2 * 2x + x * 2x) = x + 12
(-4x + 2x2) = x + 12

Reorder the terms:
-4x + 2x2 = 12 + x

Solving
-4x + 2x2 = 12 + x

Solving for variable 'x'.

Reorder the terms:
-12 + -4x + -1x + 2x2 = 12 + x + -12 + -1x

Combine like terms: -4x + -1x = -5x
-12 + -5x + 2x2 = 12 + x + -12 + -1x

Reorder the terms:
-12 + -5x + 2x2 = 12 + -12 + x + -1x

Combine like terms: 12 + -12 = 0
-12 + -5x + 2x2 = 0 + x + -1x
-12 + -5x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-12 + -5x + 2x2 = 0

Factor a trinomial.
(-3 + -2x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-1.5, 4}