(8+2x)(22+2x)=480

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Solution for (8+2x)(22+2x)=480 equation: 


Simplifying
(8 + 2x)(22 + 2x) = 480

Multiply (8 + 2x) * (22 + 2x)
(8(22 + 2x) + 2x * (22 + 2x)) = 480
((22 * 8 + 2x * 8) + 2x * (22 + 2x)) = 480
((176 + 16x) + 2x * (22 + 2x)) = 480
(176 + 16x + (22 * 2x + 2x * 2x)) = 480
(176 + 16x + (44x + 4x2)) = 480

Combine like terms: 16x + 44x = 60x
(176 + 60x + 4x2) = 480

Solving
176 + 60x + 4x2 = 480

Solving for variable 'x'.

Reorder the terms:
176 + -480 + 60x + 4x2 = 480 + -480

Combine like terms: 176 + -480 = -304
-304 + 60x + 4x2 = 480 + -480

Combine like terms: 480 + -480 = 0
-304 + 60x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-76 + 15x + x2) = 0

Factor a trinomial.
4((-19 + -1x)(4 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-19 + -1x)' equal to zero and attempt to solve:

Simplifying
-19 + -1x = 0

Solving
-19 + -1x = 0

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

Add '19' to each side of the equation.
-19 + 19 + -1x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -1x = 0 + 19
-1x = 0 + 19

Combine like terms: 0 + 19 = 19
-1x = 19

Divide each side by '-1'.
x = -19

Simplifying
x = -19

Subproblem 2
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
Solution
x = {-19, 4}

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