(20+2x)(24+2x)=896

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Solution for (20+2x)(24+2x)=896 equation: 


Simplifying
(20 + 2x)(24 + 2x) = 896

Multiply (20 + 2x) * (24 + 2x)
(20(24 + 2x) + 2x * (24 + 2x)) = 896
((24 * 20 + 2x * 20) + 2x * (24 + 2x)) = 896
((480 + 40x) + 2x * (24 + 2x)) = 896
(480 + 40x + (24 * 2x + 2x * 2x)) = 896
(480 + 40x + (48x + 4x2)) = 896

Combine like terms: 40x + 48x = 88x
(480 + 88x + 4x2) = 896

Solving
480 + 88x + 4x2 = 896

Solving for variable 'x'.

Reorder the terms:
480 + -896 + 88x + 4x2 = 896 + -896

Combine like terms: 480 + -896 = -416
-416 + 88x + 4x2 = 896 + -896

Combine like terms: 896 + -896 = 0
-416 + 88x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-104 + 22x + x2) = 0

Factor a trinomial.
4((-26 + -1x)(4 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-26 + -1x)' equal to zero and attempt to solve:

Simplifying
-26 + -1x = 0

Solving
-26 + -1x = 0

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

Add '26' to each side of the equation.
-26 + 26 + -1x = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -1x = 0 + 26
-1x = 0 + 26

Combine like terms: 0 + 26 = 26
-1x = 26

Divide each side by '-1'.
x = -26

Simplifying
x = -26

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 = {-26, 4}

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