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

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


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

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

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

Multiply (-4 + x) * (2 + x)
0 = (-4(2 + x) + x(2 + x))
0 = ((2 * -4 + x * -4) + x(2 + x))
0 = ((-8 + -4x) + x(2 + x))
0 = (-8 + -4x + (2 * x + x * x))
0 = (-8 + -4x + (2x + x2))

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

Solving
0 = -8 + -2x + x2

Solving for variable 'x'.

Combine like terms: 0 + 8 = 8
8 + 2x + -1x2 = -8 + -2x + x2 + 8 + 2x + -1x2

Reorder the terms:
8 + 2x + -1x2 = -8 + 8 + -2x + 2x + x2 + -1x2

Combine like terms: -8 + 8 = 0
8 + 2x + -1x2 = 0 + -2x + 2x + x2 + -1x2
8 + 2x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
8 + 2x + -1x2 = 0 + x2 + -1x2
8 + 2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8 + 2x + -1x2 = 0

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


Subproblem 1
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

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {4, -2}

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