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

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


Simplifying
(x + -6)(x2 + -5x + 2) = x(x + -6)(x + -5) + 6

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

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

Multiply (-6 + x) * (2 + -5x + x2)
(-6(2 + -5x + x2) + x(2 + -5x + x2)) = x(x + -6)(x + -5) + 6
((2 * -6 + -5x * -6 + x2 * -6) + x(2 + -5x + x2)) = x(x + -6)(x + -5) + 6
((-12 + 30x + -6x2) + x(2 + -5x + x2)) = x(x + -6)(x + -5) + 6
(-12 + 30x + -6x2 + (2 * x + -5x * x + x2 * x)) = x(x + -6)(x + -5) + 6
(-12 + 30x + -6x2 + (2x + -5x2 + x3)) = x(x + -6)(x + -5) + 6

Reorder the terms:
(-12 + 30x + 2x + -6x2 + -5x2 + x3) = x(x + -6)(x + -5) + 6

Combine like terms: 30x + 2x = 32x
(-12 + 32x + -6x2 + -5x2 + x3) = x(x + -6)(x + -5) + 6

Combine like terms: -6x2 + -5x2 = -11x2
(-12 + 32x + -11x2 + x3) = x(x + -6)(x + -5) + 6

Reorder the terms:
-12 + 32x + -11x2 + x3 = x(-6 + x)(x + -5) + 6

Reorder the terms:
-12 + 32x + -11x2 + x3 = x(-6 + x)(-5 + x) + 6

Multiply (-6 + x) * (-5 + x)
-12 + 32x + -11x2 + x3 = x(-6(-5 + x) + x(-5 + x)) + 6
-12 + 32x + -11x2 + x3 = x((-5 * -6 + x * -6) + x(-5 + x)) + 6
-12 + 32x + -11x2 + x3 = x((30 + -6x) + x(-5 + x)) + 6
-12 + 32x + -11x2 + x3 = x(30 + -6x + (-5 * x + x * x)) + 6
-12 + 32x + -11x2 + x3 = x(30 + -6x + (-5x + x2)) + 6

Combine like terms: -6x + -5x = -11x
-12 + 32x + -11x2 + x3 = x(30 + -11x + x2) + 6
-12 + 32x + -11x2 + x3 = (30 * x + -11x * x + x2 * x) + 6
-12 + 32x + -11x2 + x3 = (30x + -11x2 + x3) + 6

Reorder the terms:
-12 + 32x + -11x2 + x3 = 6 + 30x + -11x2 + x3

Add '11x2' to each side of the equation.
-12 + 32x + -11x2 + 11x2 + x3 = 6 + 30x + -11x2 + 11x2 + x3

Combine like terms: -11x2 + 11x2 = 0
-12 + 32x + 0 + x3 = 6 + 30x + -11x2 + 11x2 + x3
-12 + 32x + x3 = 6 + 30x + -11x2 + 11x2 + x3

Combine like terms: -11x2 + 11x2 = 0
-12 + 32x + x3 = 6 + 30x + 0 + x3
-12 + 32x + x3 = 6 + 30x + x3

Add '-1x3' to each side of the equation.
-12 + 32x + x3 + -1x3 = 6 + 30x + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-12 + 32x + 0 = 6 + 30x + x3 + -1x3
-12 + 32x = 6 + 30x + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-12 + 32x = 6 + 30x + 0
-12 + 32x = 6 + 30x

Solving
-12 + 32x = 6 + 30x

Solving for variable 'x'.

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

Add '-30x' to each side of the equation.
-12 + 32x + -30x = 6 + 30x + -30x

Combine like terms: 32x + -30x = 2x
-12 + 2x = 6 + 30x + -30x

Combine like terms: 30x + -30x = 0
-12 + 2x = 6 + 0
-12 + 2x = 6

Add '12' to each side of the equation.
-12 + 12 + 2x = 6 + 12

Combine like terms: -12 + 12 = 0
0 + 2x = 6 + 12
2x = 6 + 12

Combine like terms: 6 + 12 = 18
2x = 18

Divide each side by '2'.
x = 9

Simplifying
x = 9

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