(18+2x)(10+2x)=468

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Solution for (18+2x)(10+2x)=468 equation: 


Simplifying
(18 + 2x)(10 + 2x) = 468

Multiply (18 + 2x) * (10 + 2x)
(18(10 + 2x) + 2x * (10 + 2x)) = 468
((10 * 18 + 2x * 18) + 2x * (10 + 2x)) = 468
((180 + 36x) + 2x * (10 + 2x)) = 468
(180 + 36x + (10 * 2x + 2x * 2x)) = 468
(180 + 36x + (20x + 4x2)) = 468

Combine like terms: 36x + 20x = 56x
(180 + 56x + 4x2) = 468

Solving
180 + 56x + 4x2 = 468

Solving for variable 'x'.

Reorder the terms:
180 + -468 + 56x + 4x2 = 468 + -468

Combine like terms: 180 + -468 = -288
-288 + 56x + 4x2 = 468 + -468

Combine like terms: 468 + -468 = 0
-288 + 56x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-72 + 14x + x2) = 0

Factor a trinomial.
4((-18 + -1x)(4 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-18 + -1x)' equal to zero and attempt to solve:

Simplifying
-18 + -1x = 0

Solving
-18 + -1x = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1x = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1x = 0 + 18
-1x = 0 + 18

Combine like terms: 0 + 18 = 18
-1x = 18

Divide each side by '-1'.
x = -18

Simplifying
x = -18

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-18, 4}

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