(10+2x)(18+2x)=384

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Solution for (10+2x)(18+2x)=384 equation:


Simplifying
(10 + 2x)(18 + 2x) = 384

Multiply (10 + 2x) * (18 + 2x)
(10(18 + 2x) + 2x * (18 + 2x)) = 384
((18 * 10 + 2x * 10) + 2x * (18 + 2x)) = 384
((180 + 20x) + 2x * (18 + 2x)) = 384
(180 + 20x + (18 * 2x + 2x * 2x)) = 384
(180 + 20x + (36x + 4x2)) = 384

Combine like terms: 20x + 36x = 56x
(180 + 56x + 4x2) = 384

Solving
180 + 56x + 4x2 = 384

Solving for variable 'x'.

Reorder the terms:
180 + -384 + 56x + 4x2 = 384 + -384

Combine like terms: 180 + -384 = -204
-204 + 56x + 4x2 = 384 + -384

Combine like terms: 384 + -384 = 0
-204 + 56x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-51 + 14x + x2) = 0

Factor a trinomial.
4((-17 + -1x)(3 + -1x)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-17 + -1x)' equal to zero and attempt to solve: Simplifying -17 + -1x = 0 Solving -17 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + -1x = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -1x = 0 + 17 -1x = 0 + 17 Combine like terms: 0 + 17 = 17 -1x = 17 Divide each side by '-1'. x = -17 Simplifying x = -17

Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {-17, 3}

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