(y-4)(y-4)=64

Solution for (y-4)(y-4)=64 equation:

Simplifying
(y + -4)(y + -4) = 64

Reorder the terms:
(-4 + y)(y + -4) = 64

Reorder the terms:
(-4 + y)(-4 + y) = 64

Multiply (-4 + y) * (-4 + y)
(-4(-4 + y) + y(-4 + y)) = 64
((-4 * -4 + y * -4) + y(-4 + y)) = 64
((16 + -4y) + y(-4 + y)) = 64
(16 + -4y + (-4 * y + y * y)) = 64
(16 + -4y + (-4y + y2)) = 64

Combine like terms: -4y + -4y = -8y
(16 + -8y + y2) = 64

Solving
16 + -8y + y2 = 64

Solving for variable 'y'.

Reorder the terms:
16 + -64 + -8y + y2 = 64 + -64

Combine like terms: 16 + -64 = -48
-48 + -8y + y2 = 64 + -64

Combine like terms: 64 + -64 = 0
-48 + -8y + y2 = 0

Factor a trinomial.
(-4 + -1y)(12 + -1y) = 0

Subproblem 1
Set the factor '(-4 + -1y)' equal to zero and attempt to solve:

Simplifying
-4 + -1y = 0

Solving
-4 + -1y = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1y = 0 + 4
-1y = 0 + 4

Combine like terms: 0 + 4 = 4
-1y = 4

Divide each side by '-1'.
y = -4

Simplifying
y = -4
Subproblem 2
Set the factor '(12 + -1y)' equal to zero and attempt to solve:

Simplifying
12 + -1y = 0

Solving
12 + -1y = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1y = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1y = 0 + -12
-1y = 0 + -12

Combine like terms: 0 + -12 = -12
-1y = -12

Divide each side by '-1'.
y = 12

Simplifying
y = 12
Solution
y = {-4, 12}