(x-2)(x-5)=18

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Solution for (x-2)(x-5)=18 equation: 


Simplifying
(x + -2)(x + -5) = 18

Reorder the terms:
(-2 + x)(x + -5) = 18

Reorder the terms:
(-2 + x)(-5 + x) = 18

Multiply (-2 + x) * (-5 + x)
(-2(-5 + x) + x(-5 + x)) = 18
((-5 * -2 + x * -2) + x(-5 + x)) = 18
((10 + -2x) + x(-5 + x)) = 18
(10 + -2x + (-5 * x + x * x)) = 18
(10 + -2x + (-5x + x2)) = 18

Combine like terms: -2x + -5x = -7x
(10 + -7x + x2) = 18

Solving
10 + -7x + x2 = 18

Solving for variable 'x'.

Reorder the terms:
10 + -18 + -7x + x2 = 18 + -18

Combine like terms: 10 + -18 = -8
-8 + -7x + x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-8 + -7x + x2 = 0

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


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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1

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 = {-1, 8}

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