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

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


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

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

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

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

Combine like terms: 5x + 4x = 9x
(20 + 9x + x2) = (x + -1)(x + -5)

Reorder the terms:
20 + 9x + x2 = (-1 + x)(x + -5)

Reorder the terms:
20 + 9x + x2 = (-1 + x)(-5 + x)

Multiply (-1 + x) * (-5 + x)
20 + 9x + x2 = (-1(-5 + x) + x(-5 + x))
20 + 9x + x2 = ((-5 * -1 + x * -1) + x(-5 + x))
20 + 9x + x2 = ((5 + -1x) + x(-5 + x))
20 + 9x + x2 = (5 + -1x + (-5 * x + x * x))
20 + 9x + x2 = (5 + -1x + (-5x + x2))

Combine like terms: -1x + -5x = -6x
20 + 9x + x2 = (5 + -6x + x2)

Add '-1x2' to each side of the equation.
20 + 9x + x2 + -1x2 = 5 + -6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
20 + 9x + 0 = 5 + -6x + x2 + -1x2
20 + 9x = 5 + -6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
20 + 9x = 5 + -6x + 0
20 + 9x = 5 + -6x

Solving
20 + 9x = 5 + -6x

Solving for variable 'x'.

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

Add '6x' to each side of the equation.
20 + 9x + 6x = 5 + -6x + 6x

Combine like terms: 9x + 6x = 15x
20 + 15x = 5 + -6x + 6x

Combine like terms: -6x + 6x = 0
20 + 15x = 5 + 0
20 + 15x = 5

Add '-20' to each side of the equation.
20 + -20 + 15x = 5 + -20

Combine like terms: 20 + -20 = 0
0 + 15x = 5 + -20
15x = 5 + -20

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

Divide each side by '15'.
x = -1

Simplifying
x = -1

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