(20+x)(12+x)-240=228

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Solution for (20+x)(12+x)-240=228 equation:


Simplifying
(20 + x)(12 + x) + -240 = 228

Multiply (20 + x) * (12 + x)
(20(12 + x) + x(12 + x)) + -240 = 228
((12 * 20 + x * 20) + x(12 + x)) + -240 = 228
((240 + 20x) + x(12 + x)) + -240 = 228
(240 + 20x + (12 * x + x * x)) + -240 = 228
(240 + 20x + (12x + x2)) + -240 = 228

Combine like terms: 20x + 12x = 32x
(240 + 32x + x2) + -240 = 228

Reorder the terms:
240 + -240 + 32x + x2 = 228

Combine like terms: 240 + -240 = 0
0 + 32x + x2 = 228
32x + x2 = 228

Solving
32x + x2 = 228

Solving for variable 'x'.

Reorder the terms:
-228 + 32x + x2 = 228 + -228

Combine like terms: 228 + -228 = 0
-228 + 32x + x2 = 0

Factor a trinomial.
(-38 + -1x)(6 + -1x) = 0

Subproblem 1

Set the factor '(-38 + -1x)' equal to zero and attempt to solve: Simplifying -38 + -1x = 0 Solving -38 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '38' to each side of the equation. -38 + 38 + -1x = 0 + 38 Combine like terms: -38 + 38 = 0 0 + -1x = 0 + 38 -1x = 0 + 38 Combine like terms: 0 + 38 = 38 -1x = 38 Divide each side by '-1'. x = -38 Simplifying x = -38

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 = {-38, 6}

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