(12+x)(14+x)=288

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Solution for (12+x)(14+x)=288 equation: 


Simplifying
(12 + x)(14 + x) = 288

Multiply (12 + x) * (14 + x)
(12(14 + x) + x(14 + x)) = 288
((14 * 12 + x * 12) + x(14 + x)) = 288
((168 + 12x) + x(14 + x)) = 288
(168 + 12x + (14 * x + x * x)) = 288
(168 + 12x + (14x + x2)) = 288

Combine like terms: 12x + 14x = 26x
(168 + 26x + x2) = 288

Solving
168 + 26x + x2 = 288

Solving for variable 'x'.

Reorder the terms:
168 + -288 + 26x + x2 = 288 + -288

Combine like terms: 168 + -288 = -120
-120 + 26x + x2 = 288 + -288

Combine like terms: 288 + -288 = 0
-120 + 26x + x2 = 0

Factor a trinomial.
(-30 + -1x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-30 + -1x)' equal to zero and attempt to solve:

Simplifying
-30 + -1x = 0

Solving
-30 + -1x = 0

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

Add '30' to each side of the equation.
-30 + 30 + -1x = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -1x = 0 + 30
-1x = 0 + 30

Combine like terms: 0 + 30 = 30
-1x = 30

Divide each side by '-1'.
x = -30

Simplifying
x = -30

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-30, 4}

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