(x-4)(x+2)=(x-5)(x-6)

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Solution for (x-4)(x+2)=(x-5)(x-6) equation: 


Simplifying
(x + -4)(x + 2) = (x + -5)(x + -6)

Reorder the terms:
(-4 + x)(x + 2) = (x + -5)(x + -6)

Reorder the terms:
(-4 + x)(2 + x) = (x + -5)(x + -6)

Multiply (-4 + x) * (2 + x)
(-4(2 + x) + x(2 + x)) = (x + -5)(x + -6)
((2 * -4 + x * -4) + x(2 + x)) = (x + -5)(x + -6)
((-8 + -4x) + x(2 + x)) = (x + -5)(x + -6)
(-8 + -4x + (2 * x + x * x)) = (x + -5)(x + -6)
(-8 + -4x + (2x + x2)) = (x + -5)(x + -6)

Combine like terms: -4x + 2x = -2x
(-8 + -2x + x2) = (x + -5)(x + -6)

Reorder the terms:
-8 + -2x + x2 = (-5 + x)(x + -6)

Reorder the terms:
-8 + -2x + x2 = (-5 + x)(-6 + x)

Multiply (-5 + x) * (-6 + x)
-8 + -2x + x2 = (-5(-6 + x) + x(-6 + x))
-8 + -2x + x2 = ((-6 * -5 + x * -5) + x(-6 + x))
-8 + -2x + x2 = ((30 + -5x) + x(-6 + x))
-8 + -2x + x2 = (30 + -5x + (-6 * x + x * x))
-8 + -2x + x2 = (30 + -5x + (-6x + x2))

Combine like terms: -5x + -6x = -11x
-8 + -2x + x2 = (30 + -11x + x2)

Add '-1x2' to each side of the equation.
-8 + -2x + x2 + -1x2 = 30 + -11x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-8 + -2x + 0 = 30 + -11x + x2 + -1x2
-8 + -2x = 30 + -11x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-8 + -2x = 30 + -11x + 0
-8 + -2x = 30 + -11x

Solving
-8 + -2x = 30 + -11x

Solving for variable 'x'.

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

Add '11x' to each side of the equation.
-8 + -2x + 11x = 30 + -11x + 11x

Combine like terms: -2x + 11x = 9x
-8 + 9x = 30 + -11x + 11x

Combine like terms: -11x + 11x = 0
-8 + 9x = 30 + 0
-8 + 9x = 30

Add '8' to each side of the equation.
-8 + 8 + 9x = 30 + 8

Combine like terms: -8 + 8 = 0
0 + 9x = 30 + 8
9x = 30 + 8

Combine like terms: 30 + 8 = 38
9x = 38

Divide each side by '9'.
x = 4.222222222

Simplifying
x = 4.222222222

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