(x-4)(x-1)=(x-7)(x+5)

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Solution for (x-4)(x-1)=(x-7)(x+5) equation: 


Simplifying
(x + -4)(x + -1) = (x + -7)(x + 5)

Reorder the terms:
(-4 + x)(x + -1) = (x + -7)(x + 5)

Reorder the terms:
(-4 + x)(-1 + x) = (x + -7)(x + 5)

Multiply (-4 + x) * (-1 + x)
(-4(-1 + x) + x(-1 + x)) = (x + -7)(x + 5)
((-1 * -4 + x * -4) + x(-1 + x)) = (x + -7)(x + 5)
((4 + -4x) + x(-1 + x)) = (x + -7)(x + 5)
(4 + -4x + (-1 * x + x * x)) = (x + -7)(x + 5)
(4 + -4x + (-1x + x2)) = (x + -7)(x + 5)

Combine like terms: -4x + -1x = -5x
(4 + -5x + x2) = (x + -7)(x + 5)

Reorder the terms:
4 + -5x + x2 = (-7 + x)(x + 5)

Reorder the terms:
4 + -5x + x2 = (-7 + x)(5 + x)

Multiply (-7 + x) * (5 + x)
4 + -5x + x2 = (-7(5 + x) + x(5 + x))
4 + -5x + x2 = ((5 * -7 + x * -7) + x(5 + x))
4 + -5x + x2 = ((-35 + -7x) + x(5 + x))
4 + -5x + x2 = (-35 + -7x + (5 * x + x * x))
4 + -5x + x2 = (-35 + -7x + (5x + x2))

Combine like terms: -7x + 5x = -2x
4 + -5x + x2 = (-35 + -2x + x2)

Add '-1x2' to each side of the equation.
4 + -5x + x2 + -1x2 = -35 + -2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4 + -5x + 0 = -35 + -2x + x2 + -1x2
4 + -5x = -35 + -2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4 + -5x = -35 + -2x + 0
4 + -5x = -35 + -2x

Solving
4 + -5x = -35 + -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.
4 + -5x + 2x = -35 + -2x + 2x

Combine like terms: -5x + 2x = -3x
4 + -3x = -35 + -2x + 2x

Combine like terms: -2x + 2x = 0
4 + -3x = -35 + 0
4 + -3x = -35

Add '-4' to each side of the equation.
4 + -4 + -3x = -35 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = -35 + -4
-3x = -35 + -4

Combine like terms: -35 + -4 = -39
-3x = -39

Divide each side by '-3'.
x = 13

Simplifying
x = 13

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