(x-5)(x-2)=130

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Solution for (x-5)(x-2)=130 equation: 


Simplifying
(x + -5)(x + -2) = 130

Reorder the terms:
(-5 + x)(x + -2) = 130

Reorder the terms:
(-5 + x)(-2 + x) = 130

Multiply (-5 + x) * (-2 + x)
(-5(-2 + x) + x(-2 + x)) = 130
((-2 * -5 + x * -5) + x(-2 + x)) = 130
((10 + -5x) + x(-2 + x)) = 130
(10 + -5x + (-2 * x + x * x)) = 130
(10 + -5x + (-2x + x2)) = 130

Combine like terms: -5x + -2x = -7x
(10 + -7x + x2) = 130

Solving
10 + -7x + x2 = 130

Solving for variable 'x'.

Reorder the terms:
10 + -130 + -7x + x2 = 130 + -130

Combine like terms: 10 + -130 = -120
-120 + -7x + x2 = 130 + -130

Combine like terms: 130 + -130 = 0
-120 + -7x + x2 = 0

Factor a trinomial.
(-8 + -1x)(15 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {-8, 15}

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