(x+5)(x-5)=(2x+2)(x-5)

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Solution for (x+5)(x-5)=(2x+2)(x-5) equation: 


Simplifying
(x + 5)(x + -5) = (2x + 2)(x + -5)

Reorder the terms:
(5 + x)(x + -5) = (2x + 2)(x + -5)

Reorder the terms:
(5 + x)(-5 + x) = (2x + 2)(x + -5)

Multiply (5 + x) * (-5 + x)
(5(-5 + x) + x(-5 + x)) = (2x + 2)(x + -5)
((-5 * 5 + x * 5) + x(-5 + x)) = (2x + 2)(x + -5)
((-25 + 5x) + x(-5 + x)) = (2x + 2)(x + -5)
(-25 + 5x + (-5 * x + x * x)) = (2x + 2)(x + -5)
(-25 + 5x + (-5x + x2)) = (2x + 2)(x + -5)

Combine like terms: 5x + -5x = 0
(-25 + 0 + x2) = (2x + 2)(x + -5)
(-25 + x2) = (2x + 2)(x + -5)

Reorder the terms:
-25 + x2 = (2 + 2x)(x + -5)

Reorder the terms:
-25 + x2 = (2 + 2x)(-5 + x)

Multiply (2 + 2x) * (-5 + x)
-25 + x2 = (2(-5 + x) + 2x * (-5 + x))
-25 + x2 = ((-5 * 2 + x * 2) + 2x * (-5 + x))
-25 + x2 = ((-10 + 2x) + 2x * (-5 + x))
-25 + x2 = (-10 + 2x + (-5 * 2x + x * 2x))
-25 + x2 = (-10 + 2x + (-10x + 2x2))

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

Solving
-25 + x2 = -10 + -8x + 2x2

Solving for variable 'x'.

Reorder the terms:
-25 + 10 + 8x + x2 + -2x2 = -10 + -8x + 2x2 + 10 + 8x + -2x2

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

Combine like terms: x2 + -2x2 = -1x2
-15 + 8x + -1x2 = -10 + -8x + 2x2 + 10 + 8x + -2x2

Reorder the terms:
-15 + 8x + -1x2 = -10 + 10 + -8x + 8x + 2x2 + -2x2

Combine like terms: -10 + 10 = 0
-15 + 8x + -1x2 = 0 + -8x + 8x + 2x2 + -2x2
-15 + 8x + -1x2 = -8x + 8x + 2x2 + -2x2

Combine like terms: -8x + 8x = 0
-15 + 8x + -1x2 = 0 + 2x2 + -2x2
-15 + 8x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-15 + 8x + -1x2 = 0

Factor a trinomial.
(-5 + x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 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 + x = 0 + 5

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

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

Simplifying
x = 5

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {5, 3}

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