2x+10+x+7=x*x+12x+35

Solution for 2x+10+x+7=x*x+12x+35 equation:

Simplifying
2x + 10 + x + 7 = x * x + 12x + 35

Reorder the terms:
10 + 7 + 2x + x = x * x + 12x + 35

Combine like terms: 10 + 7 = 17
17 + 2x + x = x * x + 12x + 35

Combine like terms: 2x + x = 3x
17 + 3x = x * x + 12x + 35

Multiply x * x
17 + 3x = x2 + 12x + 35

Reorder the terms:
17 + 3x = 35 + 12x + x2

Solving
17 + 3x = 35 + 12x + x2

Solving for variable 'x'.

Reorder the terms:
17 + -35 + 3x + -12x + -1x2 = 35 + 12x + x2 + -35 + -12x + -1x2

Combine like terms: 17 + -35 = -18
-18 + 3x + -12x + -1x2 = 35 + 12x + x2 + -35 + -12x + -1x2

Combine like terms: 3x + -12x = -9x
-18 + -9x + -1x2 = 35 + 12x + x2 + -35 + -12x + -1x2

Reorder the terms:
-18 + -9x + -1x2 = 35 + -35 + 12x + -12x + x2 + -1x2

Combine like terms: 35 + -35 = 0
-18 + -9x + -1x2 = 0 + 12x + -12x + x2 + -1x2
-18 + -9x + -1x2 = 12x + -12x + x2 + -1x2

Combine like terms: 12x + -12x = 0
-18 + -9x + -1x2 = 0 + x2 + -1x2
-18 + -9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-18 + -9x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(18 + 9x + x2) = 0

Factor a trinomial.
-1((6 + x)(3 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-6, -3}