(x+4)(x-2)=16

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Solution for (x+4)(x-2)=16 equation:


Simplifying
(x + 4)(x + -2) = 16

Reorder the terms:
(4 + x)(x + -2) = 16

Reorder the terms:
(4 + x)(-2 + x) = 16

Multiply (4 + x) * (-2 + x)
(4(-2 + x) + x(-2 + x)) = 16
((-2 * 4 + x * 4) + x(-2 + x)) = 16
((-8 + 4x) + x(-2 + x)) = 16
(-8 + 4x + (-2 * x + x * x)) = 16
(-8 + 4x + (-2x + x2)) = 16

Combine like terms: 4x + -2x = 2x
(-8 + 2x + x2) = 16

Solving
-8 + 2x + x2 = 16

Solving for variable 'x'.

Reorder the terms:
-8 + -16 + 2x + x2 = 16 + -16

Combine like terms: -8 + -16 = -24
-24 + 2x + x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-24 + 2x + x2 = 0

Factor a trinomial.
(-6 + -1x)(4 + -1x) = 0

Subproblem 1

Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6

Subproblem 2

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {-6, 4}

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