0=x^2+12x+35

Solution for 0=x^2+12x+35 equation:

Simplifying
0 = x2 + 12x + 35

Reorder the terms:
0 = 35 + 12x + x2

Solving
0 = 35 + 12x + x2

Solving for variable 'x'.

Combine like terms: 0 + -35 = -35
-35 + -12x + -1x2 = 35 + 12x + x2 + -35 + -12x + -1x2

Reorder the terms:
-35 + -12x + -1x2 = 35 + -35 + 12x + -12x + x2 + -1x2

Combine like terms: 35 + -35 = 0
-35 + -12x + -1x2 = 0 + 12x + -12x + x2 + -1x2
-35 + -12x + -1x2 = 12x + -12x + x2 + -1x2

Combine like terms: 12x + -12x = 0
-35 + -12x + -1x2 = 0 + x2 + -1x2
-35 + -12x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-35 + -12x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(35 + 12x + x2) = 0

Factor a trinomial.
-1((7 + x)(5 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {-7, -5}