4w^2-16w+16=64

Solution for 4w^2-16w+16=64 equation:

Simplifying
4w2 + -16w + 16 = 64

Reorder the terms:
16 + -16w + 4w2 = 64

Solving
16 + -16w + 4w2 = 64

Solving for variable 'w'.

Reorder the terms:
16 + -64 + -16w + 4w2 = 64 + -64

Combine like terms: 16 + -64 = -48
-48 + -16w + 4w2 = 64 + -64

Combine like terms: 64 + -64 = 0
-48 + -16w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + -4w + w2) = 0

Factor a trinomial.
4((-2 + -1w)(6 + -1w)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-2 + -1w)' equal to zero and attempt to solve:

Simplifying
-2 + -1w = 0

Solving
-2 + -1w = 0

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

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

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

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

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

Simplifying
w = -2
Subproblem 2
Set the factor '(6 + -1w)' equal to zero and attempt to solve:

Simplifying
6 + -1w = 0

Solving
6 + -1w = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1w = 0 + -6
-1w = 0 + -6

Combine like terms: 0 + -6 = -6
-1w = -6

Divide each side by '-1'.
w = 6

Simplifying
w = 6
Solution
w = {-2, 6}