(x-1)(x-5)=12

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Solution for (x-1)(x-5)=12 equation:


Simplifying
(x + -1)(x + -5) = 12

Reorder the terms:
(-1 + x)(x + -5) = 12

Reorder the terms:
(-1 + x)(-5 + x) = 12

Multiply (-1 + x) * (-5 + x)
(-1(-5 + x) + x(-5 + x)) = 12
((-5 * -1 + x * -1) + x(-5 + x)) = 12
((5 + -1x) + x(-5 + x)) = 12
(5 + -1x + (-5 * x + x * x)) = 12
(5 + -1x + (-5x + x2)) = 12

Combine like terms: -1x + -5x = -6x
(5 + -6x + x2) = 12

Solving
5 + -6x + x2 = 12

Solving for variable 'x'.

Reorder the terms:
5 + -12 + -6x + x2 = 12 + -12

Combine like terms: 5 + -12 = -7
-7 + -6x + x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-7 + -6x + x2 = 0

Factor a trinomial.
(-1 + -1x)(7 + -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 '(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 = {-1, 7}

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