2(x-7)(x-7)=32

Solution for 2(x-7)(x-7)=32 equation:

Simplifying
2(x + -7)(x + -7) = 32

Reorder the terms:
2(-7 + x)(x + -7) = 32

Reorder the terms:
2(-7 + x)(-7 + x) = 32

Multiply (-7 + x) * (-7 + x)
2(-7(-7 + x) + x(-7 + x)) = 32
2((-7 * -7 + x * -7) + x(-7 + x)) = 32
2((49 + -7x) + x(-7 + x)) = 32
2(49 + -7x + (-7 * x + x * x)) = 32
2(49 + -7x + (-7x + x2)) = 32

Combine like terms: -7x + -7x = -14x
2(49 + -14x + x2) = 32
(49 * 2 + -14x * 2 + x2 * 2) = 32
(98 + -28x + 2x2) = 32

Solving
98 + -28x + 2x2 = 32

Solving for variable 'x'.

Reorder the terms:
98 + -32 + -28x + 2x2 = 32 + -32

Combine like terms: 98 + -32 = 66
66 + -28x + 2x2 = 32 + -32

Combine like terms: 32 + -32 = 0
66 + -28x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(33 + -14x + x2) = 0

Factor a trinomial.
2((3 + -1x)(11 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {3, 11}