(x+1)(x-5)=(x+5)(x-4)

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Solution for (x+1)(x-5)=(x+5)(x-4) equation: 


Simplifying
(x + 1)(x + -5) = (x + 5)(x + -4)

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

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

Multiply (1 + x) * (-5 + x)
(1(-5 + x) + x(-5 + x)) = (x + 5)(x + -4)
((-5 * 1 + x * 1) + x(-5 + x)) = (x + 5)(x + -4)
((-5 + 1x) + x(-5 + x)) = (x + 5)(x + -4)
(-5 + 1x + (-5 * x + x * x)) = (x + 5)(x + -4)
(-5 + 1x + (-5x + x2)) = (x + 5)(x + -4)

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

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

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

Multiply (5 + x) * (-4 + x)
-5 + -4x + x2 = (5(-4 + x) + x(-4 + x))
-5 + -4x + x2 = ((-4 * 5 + x * 5) + x(-4 + x))
-5 + -4x + x2 = ((-20 + 5x) + x(-4 + x))
-5 + -4x + x2 = (-20 + 5x + (-4 * x + x * x))
-5 + -4x + x2 = (-20 + 5x + (-4x + x2))

Combine like terms: 5x + -4x = 1x
-5 + -4x + x2 = (-20 + 1x + x2)

Add '-1x2' to each side of the equation.
-5 + -4x + x2 + -1x2 = -20 + 1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-5 + -4x + 0 = -20 + 1x + x2 + -1x2
-5 + -4x = -20 + 1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-5 + -4x = -20 + 1x + 0
-5 + -4x = -20 + 1x

Solving
-5 + -4x = -20 + 1x

Solving for variable 'x'.

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

Add '-1x' to each side of the equation.
-5 + -4x + -1x = -20 + 1x + -1x

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

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

Add '5' to each side of the equation.
-5 + 5 + -5x = -20 + 5

Combine like terms: -5 + 5 = 0
0 + -5x = -20 + 5
-5x = -20 + 5

Combine like terms: -20 + 5 = -15
-5x = -15

Divide each side by '-5'.
x = 3

Simplifying
x = 3

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