(18+2x)(30+2x)=1408

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Solution for (18+2x)(30+2x)=1408 equation: 


Simplifying
(18 + 2x)(30 + 2x) = 1408

Multiply (18 + 2x) * (30 + 2x)
(18(30 + 2x) + 2x * (30 + 2x)) = 1408
((30 * 18 + 2x * 18) + 2x * (30 + 2x)) = 1408
((540 + 36x) + 2x * (30 + 2x)) = 1408
(540 + 36x + (30 * 2x + 2x * 2x)) = 1408
(540 + 36x + (60x + 4x2)) = 1408

Combine like terms: 36x + 60x = 96x
(540 + 96x + 4x2) = 1408

Solving
540 + 96x + 4x2 = 1408

Solving for variable 'x'.

Reorder the terms:
540 + -1408 + 96x + 4x2 = 1408 + -1408

Combine like terms: 540 + -1408 = -868
-868 + 96x + 4x2 = 1408 + -1408

Combine like terms: 1408 + -1408 = 0
-868 + 96x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-217 + 24x + x2) = 0

Factor a trinomial.
4((-31 + -1x)(7 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-31 + -1x)' equal to zero and attempt to solve:

Simplifying
-31 + -1x = 0

Solving
-31 + -1x = 0

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

Add '31' to each side of the equation.
-31 + 31 + -1x = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -1x = 0 + 31
-1x = 0 + 31

Combine like terms: 0 + 31 = 31
-1x = 31

Divide each side by '-1'.
x = -31

Simplifying
x = -31

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-31, 7}

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