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

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}