(22+2x)(30+2x)=2100

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Solution for (22+2x)(30+2x)=2100 equation: 


Simplifying
(22 + 2x)(30 + 2x) = 2100

Multiply (22 + 2x) * (30 + 2x)
(22(30 + 2x) + 2x * (30 + 2x)) = 2100
((30 * 22 + 2x * 22) + 2x * (30 + 2x)) = 2100
((660 + 44x) + 2x * (30 + 2x)) = 2100
(660 + 44x + (30 * 2x + 2x * 2x)) = 2100
(660 + 44x + (60x + 4x2)) = 2100

Combine like terms: 44x + 60x = 104x
(660 + 104x + 4x2) = 2100

Solving
660 + 104x + 4x2 = 2100

Solving for variable 'x'.

Reorder the terms:
660 + -2100 + 104x + 4x2 = 2100 + -2100

Combine like terms: 660 + -2100 = -1440
-1440 + 104x + 4x2 = 2100 + -2100

Combine like terms: 2100 + -2100 = 0
-1440 + 104x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-360 + 26x + x2) = 0

Factor a trinomial.
4((-36 + -1x)(10 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-36 + -1x)' equal to zero and attempt to solve:

Simplifying
-36 + -1x = 0

Solving
-36 + -1x = 0

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

Add '36' to each side of the equation.
-36 + 36 + -1x = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -1x = 0 + 36
-1x = 0 + 36

Combine like terms: 0 + 36 = 36
-1x = 36

Divide each side by '-1'.
x = -36

Simplifying
x = -36

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-36, 10}

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