(x+8)(x+10)=224

Solution for (x+8)(x+10)=224 equation:

Simplifying
(x + 8)(x + 10) = 224

Reorder the terms:
(8 + x)(x + 10) = 224

Reorder the terms:
(8 + x)(10 + x) = 224

Multiply (8 + x) * (10 + x)
(8(10 + x) + x(10 + x)) = 224
((10 * 8 + x * 8) + x(10 + x)) = 224
((80 + 8x) + x(10 + x)) = 224
(80 + 8x + (10 * x + x * x)) = 224
(80 + 8x + (10x + x2)) = 224

Combine like terms: 8x + 10x = 18x
(80 + 18x + x2) = 224

Solving
80 + 18x + x2 = 224

Solving for variable 'x'.

Reorder the terms:
80 + -224 + 18x + x2 = 224 + -224

Combine like terms: 80 + -224 = -144
-144 + 18x + x2 = 224 + -224

Combine like terms: 224 + -224 = 0
-144 + 18x + x2 = 0

Factor a trinomial.
(-24 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-24 + -1x)' equal to zero and attempt to solve:

Simplifying
-24 + -1x = 0

Solving
-24 + -1x = 0

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

Add '24' to each side of the equation.
-24 + 24 + -1x = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -1x = 0 + 24
-1x = 0 + 24

Combine like terms: 0 + 24 = 24
-1x = 24

Divide each side by '-1'.
x = -24

Simplifying
x = -24
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 = {-24, 6}