(20+2x)(5+2x)=184

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Solution for (20+2x)(5+2x)=184 equation: 


Simplifying
(20 + 2x)(5 + 2x) = 184

Multiply (20 + 2x) * (5 + 2x)
(20(5 + 2x) + 2x * (5 + 2x)) = 184
((5 * 20 + 2x * 20) + 2x * (5 + 2x)) = 184
((100 + 40x) + 2x * (5 + 2x)) = 184
(100 + 40x + (5 * 2x + 2x * 2x)) = 184
(100 + 40x + (10x + 4x2)) = 184

Combine like terms: 40x + 10x = 50x
(100 + 50x + 4x2) = 184

Solving
100 + 50x + 4x2 = 184

Solving for variable 'x'.

Reorder the terms:
100 + -184 + 50x + 4x2 = 184 + -184

Combine like terms: 100 + -184 = -84
-84 + 50x + 4x2 = 184 + -184

Combine like terms: 184 + -184 = 0
-84 + 50x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-42 + 25x + 2x2) = 0

Factor a trinomial.
2((-14 + -1x)(3 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-14 + -1x)' equal to zero and attempt to solve:

Simplifying
-14 + -1x = 0

Solving
-14 + -1x = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1x = 0 + 14
-1x = 0 + 14

Combine like terms: 0 + 14 = 14
-1x = 14

Divide each side by '-1'.
x = -14

Simplifying
x = -14

Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-14, 1.5}

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