2(w+7)(w+7)+32=64

Solution for 2(w+7)(w+7)+32=64 equation:

Simplifying
2(w + 7)(w + 7) + 32 = 64

Reorder the terms:
2(7 + w)(w + 7) + 32 = 64

Reorder the terms:
2(7 + w)(7 + w) + 32 = 64

Multiply (7 + w) * (7 + w)
2(7(7 + w) + w(7 + w)) + 32 = 64
2((7 * 7 + w * 7) + w(7 + w)) + 32 = 64
2((49 + 7w) + w(7 + w)) + 32 = 64
2(49 + 7w + (7 * w + w * w)) + 32 = 64
2(49 + 7w + (7w + w2)) + 32 = 64

Combine like terms: 7w + 7w = 14w
2(49 + 14w + w2) + 32 = 64
(49 * 2 + 14w * 2 + w2 * 2) + 32 = 64
(98 + 28w + 2w2) + 32 = 64

Reorder the terms:
98 + 32 + 28w + 2w2 = 64

Combine like terms: 98 + 32 = 130
130 + 28w + 2w2 = 64

Solving
130 + 28w + 2w2 = 64

Solving for variable 'w'.

Reorder the terms:
130 + -64 + 28w + 2w2 = 64 + -64

Combine like terms: 130 + -64 = 66
66 + 28w + 2w2 = 64 + -64

Combine like terms: 64 + -64 = 0
66 + 28w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(33 + 14w + w2) = 0

Factor a trinomial.
2((11 + w)(3 + w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(11 + w)' equal to zero and attempt to solve:

Simplifying
11 + w = 0

Solving
11 + w = 0

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

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

Combine like terms: 11 + -11 = 0
0 + w = 0 + -11
w = 0 + -11

Combine like terms: 0 + -11 = -11
w = -11

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

Simplifying
3 + w = 0

Solving
3 + w = 0

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

Add '-3' to each side of the equation.
3 + -3 + w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + w = 0 + -3
w = 0 + -3

Combine like terms: 0 + -3 = -3
w = -3

Simplifying
w = -3
Solution
w = {-11, -3}