(x-4)(x-4)+(x-1)(x+1)=25

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Solution for (x-4)(x-4)+(x-1)(x+1)=25 equation: 


Simplifying
(x + -4)(x + -4) + (x + -1)(x + 1) = 25

Reorder the terms:
(-4 + x)(x + -4) + (x + -1)(x + 1) = 25

Reorder the terms:
(-4 + x)(-4 + x) + (x + -1)(x + 1) = 25

Multiply (-4 + x) * (-4 + x)
(-4(-4 + x) + x(-4 + x)) + (x + -1)(x + 1) = 25
((-4 * -4 + x * -4) + x(-4 + x)) + (x + -1)(x + 1) = 25
((16 + -4x) + x(-4 + x)) + (x + -1)(x + 1) = 25
(16 + -4x + (-4 * x + x * x)) + (x + -1)(x + 1) = 25
(16 + -4x + (-4x + x2)) + (x + -1)(x + 1) = 25

Combine like terms: -4x + -4x = -8x
(16 + -8x + x2) + (x + -1)(x + 1) = 25

Reorder the terms:
16 + -8x + x2 + (-1 + x)(x + 1) = 25

Reorder the terms:
16 + -8x + x2 + (-1 + x)(1 + x) = 25

Multiply (-1 + x) * (1 + x)
16 + -8x + x2 + (-1(1 + x) + x(1 + x)) = 25
16 + -8x + x2 + ((1 * -1 + x * -1) + x(1 + x)) = 25
16 + -8x + x2 + ((-1 + -1x) + x(1 + x)) = 25
16 + -8x + x2 + (-1 + -1x + (1 * x + x * x)) = 25
16 + -8x + x2 + (-1 + -1x + (1x + x2)) = 25

Combine like terms: -1x + 1x = 0
16 + -8x + x2 + (-1 + 0 + x2) = 25
16 + -8x + x2 + (-1 + x2) = 25

Reorder the terms:
16 + -1 + -8x + x2 + x2 = 25

Combine like terms: 16 + -1 = 15
15 + -8x + x2 + x2 = 25

Combine like terms: x2 + x2 = 2x2
15 + -8x + 2x2 = 25

Solving
15 + -8x + 2x2 = 25

Solving for variable 'x'.

Reorder the terms:
15 + -25 + -8x + 2x2 = 25 + -25

Combine like terms: 15 + -25 = -10
-10 + -8x + 2x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-10 + -8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -4x + x2) = 0

Factor a trinomial.
2((-1 + -1x)(5 + -1x)) = 0

Ignore the factor 2.

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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-1, 5}

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