(50+2x)(30+2x)-2400=0

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Solution for (50+2x)(30+2x)-2400=0 equation: 


Simplifying
(50 + 2x)(30 + 2x) + -2400 = 0

Multiply (50 + 2x) * (30 + 2x)
(50(30 + 2x) + 2x * (30 + 2x)) + -2400 = 0
((30 * 50 + 2x * 50) + 2x * (30 + 2x)) + -2400 = 0
((1500 + 100x) + 2x * (30 + 2x)) + -2400 = 0
(1500 + 100x + (30 * 2x + 2x * 2x)) + -2400 = 0
(1500 + 100x + (60x + 4x2)) + -2400 = 0

Combine like terms: 100x + 60x = 160x
(1500 + 160x + 4x2) + -2400 = 0

Reorder the terms:
1500 + -2400 + 160x + 4x2 = 0

Combine like terms: 1500 + -2400 = -900
-900 + 160x + 4x2 = 0

Solving
-900 + 160x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-225 + 40x + x2) = 0

Factor a trinomial.
4((-45 + -1x)(5 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-45 + -1x)' equal to zero and attempt to solve:

Simplifying
-45 + -1x = 0

Solving
-45 + -1x = 0

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

Add '45' to each side of the equation.
-45 + 45 + -1x = 0 + 45

Combine like terms: -45 + 45 = 0
0 + -1x = 0 + 45
-1x = 0 + 45

Combine like terms: 0 + 45 = 45
-1x = 45

Divide each side by '-1'.
x = -45

Simplifying
x = -45

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 = {-45, 5}

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