3x^2+10x+11x=180

Solution for 3x^2+10x+11x=180 equation:

Simplifying
3x2 + 10x + 11x = 180

Reorder the terms:
10x + 11x + 3x2 = 180

Combine like terms: 10x + 11x = 21x
21x + 3x2 = 180

Solving
21x + 3x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 21x + 3x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 21x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-60 + 7x + x2) = 0

Factor a trinomial.
3((-12 + -1x)(5 + -1x)) = 0

Ignore the factor 3.
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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-12, 5}