(16+2x)(24+2x)=768

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Solution for (16+2x)(24+2x)=768 equation: 


Simplifying
(16 + 2x)(24 + 2x) = 768

Multiply (16 + 2x) * (24 + 2x)
(16(24 + 2x) + 2x * (24 + 2x)) = 768
((24 * 16 + 2x * 16) + 2x * (24 + 2x)) = 768
((384 + 32x) + 2x * (24 + 2x)) = 768
(384 + 32x + (24 * 2x + 2x * 2x)) = 768
(384 + 32x + (48x + 4x2)) = 768

Combine like terms: 32x + 48x = 80x
(384 + 80x + 4x2) = 768

Solving
384 + 80x + 4x2 = 768

Solving for variable 'x'.

Reorder the terms:
384 + -768 + 80x + 4x2 = 768 + -768

Combine like terms: 384 + -768 = -384
-384 + 80x + 4x2 = 768 + -768

Combine like terms: 768 + -768 = 0
-384 + 80x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-96 + 20x + x2) = 0

Factor a trinomial.
4((-24 + -1x)(4 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-24 + -1x)' equal to zero and attempt to solve:

Simplifying
-24 + -1x = 0

Solving
-24 + -1x = 0

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

Add '24' to each side of the equation.
-24 + 24 + -1x = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -1x = 0 + 24
-1x = 0 + 24

Combine like terms: 0 + 24 = 24
-1x = 24

Divide each side by '-1'.
x = -24

Simplifying
x = -24

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 = {-24, 4}

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