(x-6)(x+9)=(x+6)(x-2)

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Solution for (x-6)(x+9)=(x+6)(x-2) equation: 


Simplifying
(x + -6)(x + 9) = (x + 6)(x + -2)

Reorder the terms:
(-6 + x)(x + 9) = (x + 6)(x + -2)

Reorder the terms:
(-6 + x)(9 + x) = (x + 6)(x + -2)

Multiply (-6 + x) * (9 + x)
(-6(9 + x) + x(9 + x)) = (x + 6)(x + -2)
((9 * -6 + x * -6) + x(9 + x)) = (x + 6)(x + -2)
((-54 + -6x) + x(9 + x)) = (x + 6)(x + -2)
(-54 + -6x + (9 * x + x * x)) = (x + 6)(x + -2)
(-54 + -6x + (9x + x2)) = (x + 6)(x + -2)

Combine like terms: -6x + 9x = 3x
(-54 + 3x + x2) = (x + 6)(x + -2)

Reorder the terms:
-54 + 3x + x2 = (6 + x)(x + -2)

Reorder the terms:
-54 + 3x + x2 = (6 + x)(-2 + x)

Multiply (6 + x) * (-2 + x)
-54 + 3x + x2 = (6(-2 + x) + x(-2 + x))
-54 + 3x + x2 = ((-2 * 6 + x * 6) + x(-2 + x))
-54 + 3x + x2 = ((-12 + 6x) + x(-2 + x))
-54 + 3x + x2 = (-12 + 6x + (-2 * x + x * x))
-54 + 3x + x2 = (-12 + 6x + (-2x + x2))

Combine like terms: 6x + -2x = 4x
-54 + 3x + x2 = (-12 + 4x + x2)

Add '-1x2' to each side of the equation.
-54 + 3x + x2 + -1x2 = -12 + 4x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-54 + 3x + 0 = -12 + 4x + x2 + -1x2
-54 + 3x = -12 + 4x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-54 + 3x = -12 + 4x + 0
-54 + 3x = -12 + 4x

Solving
-54 + 3x = -12 + 4x

Solving for variable 'x'.

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

Add '-4x' to each side of the equation.
-54 + 3x + -4x = -12 + 4x + -4x

Combine like terms: 3x + -4x = -1x
-54 + -1x = -12 + 4x + -4x

Combine like terms: 4x + -4x = 0
-54 + -1x = -12 + 0
-54 + -1x = -12

Add '54' to each side of the equation.
-54 + 54 + -1x = -12 + 54

Combine like terms: -54 + 54 = 0
0 + -1x = -12 + 54
-1x = -12 + 54

Combine like terms: -12 + 54 = 42
-1x = 42

Divide each side by '-1'.
x = -42

Simplifying
x = -42

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