(x+12)(x+10)=288

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Solution for (x+12)(x+10)=288 equation:


Simplifying
(x + 12)(x + 10) = 288

Reorder the terms:
(12 + x)(x + 10) = 288

Reorder the terms:
(12 + x)(10 + x) = 288

Multiply (12 + x) * (10 + x)
(12(10 + x) + x(10 + x)) = 288
((10 * 12 + x * 12) + x(10 + x)) = 288
((120 + 12x) + x(10 + x)) = 288
(120 + 12x + (10 * x + x * x)) = 288
(120 + 12x + (10x + x2)) = 288

Combine like terms: 12x + 10x = 22x
(120 + 22x + x2) = 288

Solving
120 + 22x + x2 = 288

Solving for variable 'x'.

Reorder the terms:
120 + -288 + 22x + x2 = 288 + -288

Combine like terms: 120 + -288 = -168
-168 + 22x + x2 = 288 + -288

Combine like terms: 288 + -288 = 0
-168 + 22x + x2 = 0

Factor a trinomial.
(-28 + -1x)(6 + -1x) = 0

Subproblem 1

Set the factor '(-28 + -1x)' equal to zero and attempt to solve: Simplifying -28 + -1x = 0 Solving -28 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + -1x = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -1x = 0 + 28 -1x = 0 + 28 Combine like terms: 0 + 28 = 28 -1x = 28 Divide each side by '-1'. x = -28 Simplifying x = -28

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 = {-28, 6}

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