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

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


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

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

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

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

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

Solving
32 + 24x + 4x2 = 480

Solving for variable 'x'.

Reorder the terms:
32 + -480 + 24x + 4x2 = 480 + -480

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

Combine like terms: 480 + -480 = 0
-448 + 24x + 4x2 = 0

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

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

Ignore the factor 4.

Subproblem 1
Set the factor '(-14 + -1x)' equal to zero and attempt to solve:

Simplifying
-14 + -1x = 0

Solving
-14 + -1x = 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 + -1x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1x = 0 + 14
-1x = 0 + 14

Combine like terms: 0 + 14 = 14
-1x = 14

Divide each side by '-1'.
x = -14

Simplifying
x = -14

Subproblem 2
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
Solution
x = {-14, 8}

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