x+4=(2x+8)(x-3)

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Solution for x+4=(2x+8)(x-3) equation: 


Simplifying
x + 4 = (2x + 8)(x + -3)

Reorder the terms:
4 + x = (2x + 8)(x + -3)

Reorder the terms:
4 + x = (8 + 2x)(x + -3)

Reorder the terms:
4 + x = (8 + 2x)(-3 + x)

Multiply (8 + 2x) * (-3 + x)
4 + x = (8(-3 + x) + 2x * (-3 + x))
4 + x = ((-3 * 8 + x * 8) + 2x * (-3 + x))
4 + x = ((-24 + 8x) + 2x * (-3 + x))
4 + x = (-24 + 8x + (-3 * 2x + x * 2x))
4 + x = (-24 + 8x + (-6x + 2x2))

Combine like terms: 8x + -6x = 2x
4 + x = (-24 + 2x + 2x2)

Solving
4 + x = -24 + 2x + 2x2

Solving for variable 'x'.

Reorder the terms:
4 + 24 + x + -2x + -2x2 = -24 + 2x + 2x2 + 24 + -2x + -2x2

Combine like terms: 4 + 24 = 28
28 + x + -2x + -2x2 = -24 + 2x + 2x2 + 24 + -2x + -2x2

Combine like terms: x + -2x = -1x
28 + -1x + -2x2 = -24 + 2x + 2x2 + 24 + -2x + -2x2

Reorder the terms:
28 + -1x + -2x2 = -24 + 24 + 2x + -2x + 2x2 + -2x2

Combine like terms: -24 + 24 = 0
28 + -1x + -2x2 = 0 + 2x + -2x + 2x2 + -2x2
28 + -1x + -2x2 = 2x + -2x + 2x2 + -2x2

Combine like terms: 2x + -2x = 0
28 + -1x + -2x2 = 0 + 2x2 + -2x2
28 + -1x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
28 + -1x + -2x2 = 0

Factor a trinomial.
(7 + -2x)(4 + x) = 0


Subproblem 1
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5

Subproblem 2
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
Solution
x = {3.5, -4}

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