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

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


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

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

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

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

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

Solving
-8 + 2x + x2 = 4x

Solving for variable 'x'.

Reorder the terms:
-8 + 2x + -4x + x2 = 4x + -4x

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

Combine like terms: 4x + -4x = 0
-8 + -2x + x2 = 0

Factor a trinomial.
(-2 + -1x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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 = {-2, 4}

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