(x-1)(x-2)-12=

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Solution for (x-1)(x-2)-12= equation:


Simplifying
(x + -1)(x + -2) + -12 = 0

Reorder the terms:
(-1 + x)(x + -2) + -12 = 0

Reorder the terms:
(-1 + x)(-2 + x) + -12 = 0

Multiply (-1 + x) * (-2 + x)
(-1(-2 + x) + x(-2 + x)) + -12 = 0
((-2 * -1 + x * -1) + x(-2 + x)) + -12 = 0
((2 + -1x) + x(-2 + x)) + -12 = 0
(2 + -1x + (-2 * x + x * x)) + -12 = 0
(2 + -1x + (-2x + x2)) + -12 = 0

Combine like terms: -1x + -2x = -3x
(2 + -3x + x2) + -12 = 0

Reorder the terms:
2 + -12 + -3x + x2 = 0

Combine like terms: 2 + -12 = -10
-10 + -3x + x2 = 0

Solving
-10 + -3x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-2 + -1x)(5 + -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 '(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

Solution

x = {-2, 5}

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