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

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


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

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

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

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

Combine like terms: -2x + 4x = 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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