(x-1)(x-2)=3x+18

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Solution for (x-1)(x-2)=3x+18 equation: 


Simplifying
(x + -1)(x + -2) = 3x + 18

Reorder the terms:
(-1 + x)(x + -2) = 3x + 18

Reorder the terms:
(-1 + x)(-2 + x) = 3x + 18

Multiply (-1 + x) * (-2 + x)
(-1(-2 + x) + x(-2 + x)) = 3x + 18
((-2 * -1 + x * -1) + x(-2 + x)) = 3x + 18
((2 + -1x) + x(-2 + x)) = 3x + 18
(2 + -1x + (-2 * x + x * x)) = 3x + 18
(2 + -1x + (-2x + x2)) = 3x + 18

Combine like terms: -1x + -2x = -3x
(2 + -3x + x2) = 3x + 18

Reorder the terms:
2 + -3x + x2 = 18 + 3x

Solving
2 + -3x + x2 = 18 + 3x

Solving for variable 'x'.

Reorder the terms:
2 + -18 + -3x + -3x + x2 = 18 + 3x + -18 + -3x

Combine like terms: 2 + -18 = -16
-16 + -3x + -3x + x2 = 18 + 3x + -18 + -3x

Combine like terms: -3x + -3x = -6x
-16 + -6x + x2 = 18 + 3x + -18 + -3x

Reorder the terms:
-16 + -6x + x2 = 18 + -18 + 3x + -3x

Combine like terms: 18 + -18 = 0
-16 + -6x + x2 = 0 + 3x + -3x
-16 + -6x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-16 + -6x + x2 = 0

Factor a trinomial.
(-2 + -1x)(8 + -1x) = 0


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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 = {-2, 8}

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