(x-10)(x-2)=65

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Solution for (x-10)(x-2)=65 equation:


Simplifying
(x + -10)(x + -2) = 65

Reorder the terms:
(-10 + x)(x + -2) = 65

Reorder the terms:
(-10 + x)(-2 + x) = 65

Multiply (-10 + x) * (-2 + x)
(-10(-2 + x) + x(-2 + x)) = 65
((-2 * -10 + x * -10) + x(-2 + x)) = 65
((20 + -10x) + x(-2 + x)) = 65
(20 + -10x + (-2 * x + x * x)) = 65
(20 + -10x + (-2x + x2)) = 65

Combine like terms: -10x + -2x = -12x
(20 + -12x + x2) = 65

Solving
20 + -12x + x2 = 65

Solving for variable 'x'.

Reorder the terms:
20 + -65 + -12x + x2 = 65 + -65

Combine like terms: 20 + -65 = -45
-45 + -12x + x2 = 65 + -65

Combine like terms: 65 + -65 = 0
-45 + -12x + x2 = 0

Factor a trinomial.
(-3 + -1x)(15 + -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 '(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 = {-3, 15}

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