(x-2)(x-4)=15

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Solution for (x-2)(x-4)=15 equation:


Simplifying
(x + -2)(x + -4) = 15

Reorder the terms:
(-2 + x)(x + -4) = 15

Reorder the terms:
(-2 + x)(-4 + x) = 15

Multiply (-2 + x) * (-4 + x)
(-2(-4 + x) + x(-4 + x)) = 15
((-4 * -2 + x * -2) + x(-4 + x)) = 15
((8 + -2x) + x(-4 + x)) = 15
(8 + -2x + (-4 * x + x * x)) = 15
(8 + -2x + (-4x + x2)) = 15

Combine like terms: -2x + -4x = -6x
(8 + -6x + x2) = 15

Solving
8 + -6x + x2 = 15

Solving for variable 'x'.

Reorder the terms:
8 + -15 + -6x + x2 = 15 + -15

Combine like terms: 8 + -15 = -7
-7 + -6x + x2 = 15 + -15

Combine like terms: 15 + -15 = 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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