x^2+(x+2)(x+4)-224=0

Solution for x^2+(x+2)(x+4)-224=0 equation:

Simplifying
x2 + (x + 2)(x + 4) + -224 = 0

Reorder the terms:
x2 + (2 + x)(x + 4) + -224 = 0

Reorder the terms:
x2 + (2 + x)(4 + x) + -224 = 0

Multiply (2 + x) * (4 + x)
x2 + (2(4 + x) + x(4 + x)) + -224 = 0
x2 + ((4 * 2 + x * 2) + x(4 + x)) + -224 = 0
x2 + ((8 + 2x) + x(4 + x)) + -224 = 0
x2 + (8 + 2x + (4 * x + x * x)) + -224 = 0
x2 + (8 + 2x + (4x + x2)) + -224 = 0

Combine like terms: 2x + 4x = 6x
x2 + (8 + 6x + x2) + -224 = 0

Reorder the terms:
8 + -224 + 6x + x2 + x2 = 0

Combine like terms: 8 + -224 = -216
-216 + 6x + x2 + x2 = 0

Combine like terms: x2 + x2 = 2x2
-216 + 6x + 2x2 = 0

Solving
-216 + 6x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-108 + 3x + x2) = 0

Factor a trinomial.
2((-12 + -1x)(9 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-12, 9}