2(x-3)(x-3)=32

Solution for 2(x-3)(x-3)=32 equation:

Simplifying
2(x + -3)(x + -3) = 32

Reorder the terms:
2(-3 + x)(x + -3) = 32

Reorder the terms:
2(-3 + x)(-3 + x) = 32

Multiply (-3 + x) * (-3 + x)
2(-3(-3 + x) + x(-3 + x)) = 32
2((-3 * -3 + x * -3) + x(-3 + x)) = 32
2((9 + -3x) + x(-3 + x)) = 32
2(9 + -3x + (-3 * x + x * x)) = 32
2(9 + -3x + (-3x + x2)) = 32

Combine like terms: -3x + -3x = -6x
2(9 + -6x + x2) = 32
(9 * 2 + -6x * 2 + x2 * 2) = 32
(18 + -12x + 2x2) = 32

Solving
18 + -12x + 2x2 = 32

Solving for variable 'x'.

Reorder the terms:
18 + -32 + -12x + 2x2 = 32 + -32

Combine like terms: 18 + -32 = -14
-14 + -12x + 2x2 = 32 + -32

Combine like terms: 32 + -32 = 0
-14 + -12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -6x + x2) = 0

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

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
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, 7}