(x+1)(x-5)=(2x+5)(x-5)

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Solution for (x+1)(x-5)=(2x+5)(x-5) equation: 


Simplifying
(x + 1)(x + -5) = (2x + 5)(x + -5)

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

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

Multiply (1 + x) * (-5 + x)
(1(-5 + x) + x(-5 + x)) = (2x + 5)(x + -5)
((-5 * 1 + x * 1) + x(-5 + x)) = (2x + 5)(x + -5)
((-5 + 1x) + x(-5 + x)) = (2x + 5)(x + -5)
(-5 + 1x + (-5 * x + x * x)) = (2x + 5)(x + -5)
(-5 + 1x + (-5x + x2)) = (2x + 5)(x + -5)

Combine like terms: 1x + -5x = -4x
(-5 + -4x + x2) = (2x + 5)(x + -5)

Reorder the terms:
-5 + -4x + x2 = (5 + 2x)(x + -5)

Reorder the terms:
-5 + -4x + x2 = (5 + 2x)(-5 + x)

Multiply (5 + 2x) * (-5 + x)
-5 + -4x + x2 = (5(-5 + x) + 2x * (-5 + x))
-5 + -4x + x2 = ((-5 * 5 + x * 5) + 2x * (-5 + x))
-5 + -4x + x2 = ((-25 + 5x) + 2x * (-5 + x))
-5 + -4x + x2 = (-25 + 5x + (-5 * 2x + x * 2x))
-5 + -4x + x2 = (-25 + 5x + (-10x + 2x2))

Combine like terms: 5x + -10x = -5x
-5 + -4x + x2 = (-25 + -5x + 2x2)

Solving
-5 + -4x + x2 = -25 + -5x + 2x2

Solving for variable 'x'.

Reorder the terms:
-5 + 25 + -4x + 5x + x2 + -2x2 = -25 + -5x + 2x2 + 25 + 5x + -2x2

Combine like terms: -5 + 25 = 20
20 + -4x + 5x + x2 + -2x2 = -25 + -5x + 2x2 + 25 + 5x + -2x2

Combine like terms: -4x + 5x = 1x
20 + 1x + x2 + -2x2 = -25 + -5x + 2x2 + 25 + 5x + -2x2

Combine like terms: x2 + -2x2 = -1x2
20 + 1x + -1x2 = -25 + -5x + 2x2 + 25 + 5x + -2x2

Reorder the terms:
20 + 1x + -1x2 = -25 + 25 + -5x + 5x + 2x2 + -2x2

Combine like terms: -25 + 25 = 0
20 + 1x + -1x2 = 0 + -5x + 5x + 2x2 + -2x2
20 + 1x + -1x2 = -5x + 5x + 2x2 + -2x2

Combine like terms: -5x + 5x = 0
20 + 1x + -1x2 = 0 + 2x2 + -2x2
20 + 1x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
20 + 1x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(4 + x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

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

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {5, -4}

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