(x)(x)+12x+42=10

Solution for (x)(x)+12x+42=10 equation:

Simplifying
(x)(x) + 12x + 42 = 10

Multiply x * x
x2 + 12x + 42 = 10

Reorder the terms:
42 + 12x + x2 = 10

Solving
42 + 12x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
42 + -10 + 12x + x2 = 10 + -10

Combine like terms: 42 + -10 = 32
32 + 12x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
32 + 12x + x2 = 0

Factor a trinomial.
(8 + x)(4 + x) = 0

Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

Simplifying
x = -4
Solution
x = {-8, -4}