480=(4x+8)(x+4)

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Solution for 480=(4x+8)(x+4) equation: 


Simplifying
480 = (4x + 8)(x + 4)

Reorder the terms:
480 = (8 + 4x)(x + 4)

Reorder the terms:
480 = (8 + 4x)(4 + x)

Multiply (8 + 4x) * (4 + x)
480 = (8(4 + x) + 4x * (4 + x))
480 = ((4 * 8 + x * 8) + 4x * (4 + x))
480 = ((32 + 8x) + 4x * (4 + x))
480 = (32 + 8x + (4 * 4x + x * 4x))
480 = (32 + 8x + (16x + 4x2))

Combine like terms: 8x + 16x = 24x
480 = (32 + 24x + 4x2)

Solving
480 = 32 + 24x + 4x2

Solving for variable 'x'.

Combine like terms: 480 + -32 = 448
448 + -24x + -4x2 = 32 + 24x + 4x2 + -32 + -24x + -4x2

Reorder the terms:
448 + -24x + -4x2 = 32 + -32 + 24x + -24x + 4x2 + -4x2

Combine like terms: 32 + -32 = 0
448 + -24x + -4x2 = 0 + 24x + -24x + 4x2 + -4x2
448 + -24x + -4x2 = 24x + -24x + 4x2 + -4x2

Combine like terms: 24x + -24x = 0
448 + -24x + -4x2 = 0 + 4x2 + -4x2
448 + -24x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
448 + -24x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(112 + -6x + -1x2) = 0

Factor a trinomial.
4((8 + -1x)(14 + x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

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

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

Divide each side by '-1'.
x = 8

Simplifying
x = 8

Subproblem 2
Set the factor '(14 + x)' equal to zero and attempt to solve:

Simplifying
14 + x = 0

Solving
14 + x = 0

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

Add '-14' to each side of the equation.
14 + -14 + x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + x = 0 + -14
x = 0 + -14

Combine like terms: 0 + -14 = -14
x = -14

Simplifying
x = -14
Solution
x = {8, -14}

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