(8+2x)(24+2x)=612

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Solution for (8+2x)(24+2x)=612 equation: 


Simplifying
(8 + 2x)(24 + 2x) = 612

Multiply (8 + 2x) * (24 + 2x)
(8(24 + 2x) + 2x * (24 + 2x)) = 612
((24 * 8 + 2x * 8) + 2x * (24 + 2x)) = 612
((192 + 16x) + 2x * (24 + 2x)) = 612
(192 + 16x + (24 * 2x + 2x * 2x)) = 612
(192 + 16x + (48x + 4x2)) = 612

Combine like terms: 16x + 48x = 64x
(192 + 64x + 4x2) = 612

Solving
192 + 64x + 4x2 = 612

Solving for variable 'x'.

Reorder the terms:
192 + -612 + 64x + 4x2 = 612 + -612

Combine like terms: 192 + -612 = -420
-420 + 64x + 4x2 = 612 + -612

Combine like terms: 612 + -612 = 0
-420 + 64x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-105 + 16x + x2) = 0

Factor a trinomial.
4((-21 + -1x)(5 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-21 + -1x)' equal to zero and attempt to solve:

Simplifying
-21 + -1x = 0

Solving
-21 + -1x = 0

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

Add '21' to each side of the equation.
-21 + 21 + -1x = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -1x = 0 + 21
-1x = 0 + 21

Combine like terms: 0 + 21 = 21
-1x = 21

Divide each side by '-1'.
x = -21

Simplifying
x = -21

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-21, 5}

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