(x+1)(x-1)+(x+1)(2x-4)=0

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Solution for (x+1)(x-1)+(x+1)(2x-4)=0 equation:


Simplifying
(x + 1)(x + -1) + (x + 1)(2x + -4) = 0

Reorder the terms:
(1 + x)(x + -1) + (x + 1)(2x + -4) = 0

Reorder the terms:
(1 + x)(-1 + x) + (x + 1)(2x + -4) = 0

Multiply (1 + x) * (-1 + x)
(1(-1 + x) + x(-1 + x)) + (x + 1)(2x + -4) = 0
((-1 * 1 + x * 1) + x(-1 + x)) + (x + 1)(2x + -4) = 0
((-1 + 1x) + x(-1 + x)) + (x + 1)(2x + -4) = 0
(-1 + 1x + (-1 * x + x * x)) + (x + 1)(2x + -4) = 0
(-1 + 1x + (-1x + x2)) + (x + 1)(2x + -4) = 0

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

Reorder the terms:
-1 + x2 + (1 + x)(2x + -4) = 0

Reorder the terms:
-1 + x2 + (1 + x)(-4 + 2x) = 0

Multiply (1 + x) * (-4 + 2x)
-1 + x2 + (1(-4 + 2x) + x(-4 + 2x)) = 0
-1 + x2 + ((-4 * 1 + 2x * 1) + x(-4 + 2x)) = 0
-1 + x2 + ((-4 + 2x) + x(-4 + 2x)) = 0
-1 + x2 + (-4 + 2x + (-4 * x + 2x * x)) = 0
-1 + x2 + (-4 + 2x + (-4x + 2x2)) = 0

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

Reorder the terms:
-1 + -4 + -2x + x2 + 2x2 = 0

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

Combine like terms: x2 + 2x2 = 3x2
-5 + -2x + 3x2 = 0

Solving
-5 + -2x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -1x)(5 + -3x) = 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 '(5 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 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 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Divide each side by '-3'. x = 1.666666667 Simplifying x = 1.666666667

Solution

x = {-1, 1.666666667}

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