(20+x)*(20+2x)=832

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Solution for (20+x)*(20+2x)=832 equation:


Simplifying
(20 + x)(20 + 2x) = 832

Multiply (20 + x) * (20 + 2x)
(20(20 + 2x) + x(20 + 2x)) = 832
((20 * 20 + 2x * 20) + x(20 + 2x)) = 832
((400 + 40x) + x(20 + 2x)) = 832
(400 + 40x + (20 * x + 2x * x)) = 832
(400 + 40x + (20x + 2x2)) = 832

Combine like terms: 40x + 20x = 60x
(400 + 60x + 2x2) = 832

Solving
400 + 60x + 2x2 = 832

Solving for variable 'x'.

Reorder the terms:
400 + -832 + 60x + 2x2 = 832 + -832

Combine like terms: 400 + -832 = -432
-432 + 60x + 2x2 = 832 + -832

Combine like terms: 832 + -832 = 0
-432 + 60x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-216 + 30x + x2) = 0

Factor a trinomial.
2((-36 + -1x)(6 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-36 + -1x)' equal to zero and attempt to solve: Simplifying -36 + -1x = 0 Solving -36 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + -1x = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -1x = 0 + 36 -1x = 0 + 36 Combine like terms: 0 + 36 = 36 -1x = 36 Divide each side by '-1'. x = -36 Simplifying x = -36

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Solution

x = {-36, 6}

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