2x(x+6)=32

Solution for 2x(x+6)=32 equation:

Simplifying
2x(x + 6) = 32

Reorder the terms:
2x(6 + x) = 32
(6 * 2x + x * 2x) = 32
(12x + 2x2) = 32

Solving
12x + 2x2 = 32

Solving for variable 'x'.

Reorder the terms:
-32 + 12x + 2x2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + 6x + x2) = 0

Factor a trinomial.
2((-8 + -1x)(2 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-8, 2}