=(x+2)(x+4)

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


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

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

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

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

Combine like terms: 2x + 4x = 6x
0 = (8 + 6x + x2)

Solving
0 = 8 + 6x + x2

Solving for variable 'x'.

Combine like terms: 0 + -8 = -8
-8 + -6x + -1x2 = 8 + 6x + x2 + -8 + -6x + -1x2

Reorder the terms:
-8 + -6x + -1x2 = 8 + -8 + 6x + -6x + x2 + -1x2

Combine like terms: 8 + -8 = 0
-8 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2
-8 + -6x + -1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
-8 + -6x + -1x2 = 0 + x2 + -1x2
-8 + -6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-8 + -6x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 6x + x2) = 0

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

Ignore the factor -1.

Subproblem 1

Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 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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