(x-4)(x-4)=25

Solution for (x-4)(x-4)=25 equation:

Simplifying
(x + -4)(x + -4) = 25

Reorder the terms:
(-4 + x)(x + -4) = 25

Reorder the terms:
(-4 + x)(-4 + x) = 25

Multiply (-4 + x) * (-4 + x)
(-4(-4 + x) + x(-4 + x)) = 25
((-4 * -4 + x * -4) + x(-4 + x)) = 25
((16 + -4x) + x(-4 + x)) = 25
(16 + -4x + (-4 * x + x * x)) = 25
(16 + -4x + (-4x + x2)) = 25

Combine like terms: -4x + -4x = -8x
(16 + -8x + x2) = 25

Solving
16 + -8x + x2 = 25

Solving for variable 'x'.

Reorder the terms:
16 + -25 + -8x + x2 = 25 + -25

Combine like terms: 16 + -25 = -9
-9 + -8x + x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-9 + -8x + x2 = 0

Factor a trinomial.
(-1 + -1x)(9 + -1x) = 0

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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-1, 9}