3x^2=-36x-105

Solution for 3x^2=-36x-105 equation:

Simplifying
3x2 = -36x + -105

Reorder the terms:
3x2 = -105 + -36x

Solving
3x2 = -105 + -36x

Solving for variable 'x'.

Reorder the terms:
105 + 36x + 3x2 = -105 + -36x + 105 + 36x

Reorder the terms:
105 + 36x + 3x2 = -105 + 105 + -36x + 36x

Combine like terms: -105 + 105 = 0
105 + 36x + 3x2 = 0 + -36x + 36x
105 + 36x + 3x2 = -36x + 36x

Combine like terms: -36x + 36x = 0
105 + 36x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(35 + 12x + x2) = 0

Factor a trinomial.
3((7 + x)(5 + x)) = 0

Ignore the factor 3.
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}