(x-3)(x-2)=6(x-3)

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Solution for (x-3)(x-2)=6(x-3) equation: 


Simplifying
(x + -3)(x + -2) = 6(x + -3)

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

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

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

Combine like terms: -3x + -2x = -5x
(6 + -5x + x2) = 6(x + -3)

Reorder the terms:
6 + -5x + x2 = 6(-3 + x)
6 + -5x + x2 = (-3 * 6 + x * 6)
6 + -5x + x2 = (-18 + 6x)

Solving
6 + -5x + x2 = -18 + 6x

Solving for variable 'x'.

Reorder the terms:
6 + 18 + -5x + -6x + x2 = -18 + 6x + 18 + -6x

Combine like terms: 6 + 18 = 24
24 + -5x + -6x + x2 = -18 + 6x + 18 + -6x

Combine like terms: -5x + -6x = -11x
24 + -11x + x2 = -18 + 6x + 18 + -6x

Reorder the terms:
24 + -11x + x2 = -18 + 18 + 6x + -6x

Combine like terms: -18 + 18 = 0
24 + -11x + x2 = 0 + 6x + -6x
24 + -11x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
24 + -11x + x2 = 0

Factor a trinomial.
(3 + -1x)(8 + -1x) = 0


Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {3, 8}

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