(21+2x)(18+2x)=550

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Solution for (21+2x)(18+2x)=550 equation: 


Simplifying
(21 + 2x)(18 + 2x) = 550

Multiply (21 + 2x) * (18 + 2x)
(21(18 + 2x) + 2x * (18 + 2x)) = 550
((18 * 21 + 2x * 21) + 2x * (18 + 2x)) = 550
((378 + 42x) + 2x * (18 + 2x)) = 550
(378 + 42x + (18 * 2x + 2x * 2x)) = 550
(378 + 42x + (36x + 4x2)) = 550

Combine like terms: 42x + 36x = 78x
(378 + 78x + 4x2) = 550

Solving
378 + 78x + 4x2 = 550

Solving for variable 'x'.

Reorder the terms:
378 + -550 + 78x + 4x2 = 550 + -550

Combine like terms: 378 + -550 = -172
-172 + 78x + 4x2 = 550 + -550

Combine like terms: 550 + -550 = 0
-172 + 78x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-86 + 39x + 2x2) = 0

Factor a trinomial.
2((-43 + -2x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-43 + -2x)' equal to zero and attempt to solve:

Simplifying
-43 + -2x = 0

Solving
-43 + -2x = 0

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

Add '43' to each side of the equation.
-43 + 43 + -2x = 0 + 43

Combine like terms: -43 + 43 = 0
0 + -2x = 0 + 43
-2x = 0 + 43

Combine like terms: 0 + 43 = 43
-2x = 43

Divide each side by '-2'.
x = -21.5

Simplifying
x = -21.5

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-21.5, 2}

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