130x^2+20x-110=0

Solution for 130x^2+20x-110=0 equation:

Simplifying
130x2 + 20x + -110 = 0

Reorder the terms:
-110 + 20x + 130x2 = 0

Solving
-110 + 20x + 130x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-11 + 2x + 13x2) = 0

Factor a trinomial.
10((-1 + -1x)(11 + -13x)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1x = 0 + 1

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(11 + -13x)' equal to zero and attempt to solve:

Simplifying
11 + -13x = 0

Solving
11 + -13x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -13x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -13x = 0 + -11
-13x = 0 + -11

Combine like terms: 0 + -11 = -11
-13x = -11

Divide each side by '-13'.
x = 0.8461538462

Simplifying
x = 0.8461538462
Solution
x = {-1, 0.8461538462}