(x+2)(x-4)=2x(x-3)-13

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Solution for (x+2)(x-4)=2x(x-3)-13 equation:


Simplifying
(x + 2)(x + -4) = 2x(x + -3) + -13

Reorder the terms:
(2 + x)(x + -4) = 2x(x + -3) + -13

Reorder the terms:
(2 + x)(-4 + x) = 2x(x + -3) + -13

Multiply (2 + x) * (-4 + x)
(2(-4 + x) + x(-4 + x)) = 2x(x + -3) + -13
((-4 * 2 + x * 2) + x(-4 + x)) = 2x(x + -3) + -13
((-8 + 2x) + x(-4 + x)) = 2x(x + -3) + -13
(-8 + 2x + (-4 * x + x * x)) = 2x(x + -3) + -13
(-8 + 2x + (-4x + x2)) = 2x(x + -3) + -13

Combine like terms: 2x + -4x = -2x
(-8 + -2x + x2) = 2x(x + -3) + -13

Reorder the terms:
-8 + -2x + x2 = 2x(-3 + x) + -13
-8 + -2x + x2 = (-3 * 2x + x * 2x) + -13
-8 + -2x + x2 = (-6x + 2x2) + -13

Reorder the terms:
-8 + -2x + x2 = -13 + -6x + 2x2

Solving
-8 + -2x + x2 = -13 + -6x + 2x2

Solving for variable 'x'.

Reorder the terms:
-8 + 13 + -2x + 6x + x2 + -2x2 = -13 + -6x + 2x2 + 13 + 6x + -2x2

Combine like terms: -8 + 13 = 5
5 + -2x + 6x + x2 + -2x2 = -13 + -6x + 2x2 + 13 + 6x + -2x2

Combine like terms: -2x + 6x = 4x
5 + 4x + x2 + -2x2 = -13 + -6x + 2x2 + 13 + 6x + -2x2

Combine like terms: x2 + -2x2 = -1x2
5 + 4x + -1x2 = -13 + -6x + 2x2 + 13 + 6x + -2x2

Reorder the terms:
5 + 4x + -1x2 = -13 + 13 + -6x + 6x + 2x2 + -2x2

Combine like terms: -13 + 13 = 0
5 + 4x + -1x2 = 0 + -6x + 6x + 2x2 + -2x2
5 + 4x + -1x2 = -6x + 6x + 2x2 + -2x2

Combine like terms: -6x + 6x = 0
5 + 4x + -1x2 = 0 + 2x2 + -2x2
5 + 4x + -1x2 = 2x2 + -2x2

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

Factor a trinomial.
(5 + -1x)(1 + x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {5, -1}

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