(x-2)(x-10)=-15

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Solution for (x-2)(x-10)=-15 equation: 


Simplifying
(x + -2)(x + -10) = -15

Reorder the terms:
(-2 + x)(x + -10) = -15

Reorder the terms:
(-2 + x)(-10 + x) = -15

Multiply (-2 + x) * (-10 + x)
(-2(-10 + x) + x(-10 + x)) = -15
((-10 * -2 + x * -2) + x(-10 + x)) = -15
((20 + -2x) + x(-10 + x)) = -15
(20 + -2x + (-10 * x + x * x)) = -15
(20 + -2x + (-10x + x2)) = -15

Combine like terms: -2x + -10x = -12x
(20 + -12x + x2) = -15

Solving
20 + -12x + x2 = -15

Solving for variable 'x'.

Reorder the terms:
20 + 15 + -12x + x2 = -15 + 15

Combine like terms: 20 + 15 = 35
35 + -12x + x2 = -15 + 15

Combine like terms: -15 + 15 = 0
35 + -12x + x2 = 0

Factor a trinomial.
(5 + -1x)(7 + -1x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {5, 7}

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