(x+1)(x-1)=2(x+5)+4

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Solution for (x+1)(x-1)=2(x+5)+4 equation:


Simplifying
(x + 1)(x + -1) = 2(x + 5) + 4

Reorder the terms:
(1 + x)(x + -1) = 2(x + 5) + 4

Reorder the terms:
(1 + x)(-1 + x) = 2(x + 5) + 4

Multiply (1 + x) * (-1 + x)
(1(-1 + x) + x(-1 + x)) = 2(x + 5) + 4
((-1 * 1 + x * 1) + x(-1 + x)) = 2(x + 5) + 4
((-1 + 1x) + x(-1 + x)) = 2(x + 5) + 4
(-1 + 1x + (-1 * x + x * x)) = 2(x + 5) + 4
(-1 + 1x + (-1x + x2)) = 2(x + 5) + 4

Combine like terms: 1x + -1x = 0
(-1 + 0 + x2) = 2(x + 5) + 4
(-1 + x2) = 2(x + 5) + 4

Reorder the terms:
-1 + x2 = 2(5 + x) + 4
-1 + x2 = (5 * 2 + x * 2) + 4
-1 + x2 = (10 + 2x) + 4

Reorder the terms:
-1 + x2 = 10 + 4 + 2x

Combine like terms: 10 + 4 = 14
-1 + x2 = 14 + 2x

Solving
-1 + x2 = 14 + 2x

Solving for variable 'x'.

Reorder the terms:
-1 + -14 + -2x + x2 = 14 + 2x + -14 + -2x

Combine like terms: -1 + -14 = -15
-15 + -2x + x2 = 14 + 2x + -14 + -2x

Reorder the terms:
-15 + -2x + x2 = 14 + -14 + 2x + -2x

Combine like terms: 14 + -14 = 0
-15 + -2x + x2 = 0 + 2x + -2x
-15 + -2x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-15 + -2x + x2 = 0

Factor a trinomial.
(-3 + -1x)(5 + -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 '(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 = {-3, 5}

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