(x-2)(x-6)=5

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Solution for (x-2)(x-6)=5 equation:


Simplifying
(x + -2)(x + -6) = 5

Reorder the terms:
(-2 + x)(x + -6) = 5

Reorder the terms:
(-2 + x)(-6 + x) = 5

Multiply (-2 + x) * (-6 + x)
(-2(-6 + x) + x(-6 + x)) = 5
((-6 * -2 + x * -2) + x(-6 + x)) = 5
((12 + -2x) + x(-6 + x)) = 5
(12 + -2x + (-6 * x + x * x)) = 5
(12 + -2x + (-6x + x2)) = 5

Combine like terms: -2x + -6x = -8x
(12 + -8x + x2) = 5

Solving
12 + -8x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
12 + -5 + -8x + x2 = 5 + -5

Combine like terms: 12 + -5 = 7
7 + -8x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
7 + -8x + 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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