(20+4x)(40+4x)=2400

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Solution for (20+4x)(40+4x)=2400 equation: 


Simplifying
(20 + 4x)(40 + 4x) = 2400

Multiply (20 + 4x) * (40 + 4x)
(20(40 + 4x) + 4x * (40 + 4x)) = 2400
((40 * 20 + 4x * 20) + 4x * (40 + 4x)) = 2400
((800 + 80x) + 4x * (40 + 4x)) = 2400
(800 + 80x + (40 * 4x + 4x * 4x)) = 2400
(800 + 80x + (160x + 16x2)) = 2400

Combine like terms: 80x + 160x = 240x
(800 + 240x + 16x2) = 2400

Solving
800 + 240x + 16x2 = 2400

Solving for variable 'x'.

Reorder the terms:
800 + -2400 + 240x + 16x2 = 2400 + -2400

Combine like terms: 800 + -2400 = -1600
-1600 + 240x + 16x2 = 2400 + -2400

Combine like terms: 2400 + -2400 = 0
-1600 + 240x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-100 + 15x + x2) = 0

Factor a trinomial.
16((-20 + -1x)(5 + -1x)) = 0

Ignore the factor 16.

Subproblem 1
Set the factor '(-20 + -1x)' equal to zero and attempt to solve:

Simplifying
-20 + -1x = 0

Solving
-20 + -1x = 0

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

Add '20' to each side of the equation.
-20 + 20 + -1x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -1x = 0 + 20
-1x = 0 + 20

Combine like terms: 0 + 20 = 20
-1x = 20

Divide each side by '-1'.
x = -20

Simplifying
x = -20

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 = {-20, 5}

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