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

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


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

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

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

Multiply (4 + x) * (-5 + x)
(4(-5 + x) + x(-5 + x)) = (x + 1)(x + 1)
((-5 * 4 + x * 4) + x(-5 + x)) = (x + 1)(x + 1)
((-20 + 4x) + x(-5 + x)) = (x + 1)(x + 1)
(-20 + 4x + (-5 * x + x * x)) = (x + 1)(x + 1)
(-20 + 4x + (-5x + x2)) = (x + 1)(x + 1)

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

Reorder the terms:
-20 + -1x + x2 = (1 + x)(x + 1)

Reorder the terms:
-20 + -1x + x2 = (1 + x)(1 + x)

Multiply (1 + x) * (1 + x)
-20 + -1x + x2 = (1(1 + x) + x(1 + x))
-20 + -1x + x2 = ((1 * 1 + x * 1) + x(1 + x))
-20 + -1x + x2 = ((1 + 1x) + x(1 + x))
-20 + -1x + x2 = (1 + 1x + (1 * x + x * x))
-20 + -1x + x2 = (1 + 1x + (1x + x2))

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

Add '-1x2' to each side of the equation.
-20 + -1x + x2 + -1x2 = 1 + 2x + x2 + -1x2

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

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

Solving
-20 + -1x = 1 + 2x

Solving for variable 'x'.

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

Add '-2x' to each side of the equation.
-20 + -1x + -2x = 1 + 2x + -2x

Combine like terms: -1x + -2x = -3x
-20 + -3x = 1 + 2x + -2x

Combine like terms: 2x + -2x = 0
-20 + -3x = 1 + 0
-20 + -3x = 1

Add '20' to each side of the equation.
-20 + 20 + -3x = 1 + 20

Combine like terms: -20 + 20 = 0
0 + -3x = 1 + 20
-3x = 1 + 20

Combine like terms: 1 + 20 = 21
-3x = 21

Divide each side by '-3'.
x = -7

Simplifying
x = -7

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