0=9x^2+107x+240

Solution for 0=9x^2+107x+240 equation:

Simplifying
0 = 9x2 + 107x + 240

Reorder the terms:
0 = 240 + 107x + 9x2

Solving
0 = 240 + 107x + 9x2

Solving for variable 'x'.

Combine like terms: 0 + -240 = -240
-240 + -107x + -9x2 = 240 + 107x + 9x2 + -240 + -107x + -9x2

Reorder the terms:
-240 + -107x + -9x2 = 240 + -240 + 107x + -107x + 9x2 + -9x2

Combine like terms: 240 + -240 = 0
-240 + -107x + -9x2 = 0 + 107x + -107x + 9x2 + -9x2
-240 + -107x + -9x2 = 107x + -107x + 9x2 + -9x2

Combine like terms: 107x + -107x = 0
-240 + -107x + -9x2 = 0 + 9x2 + -9x2
-240 + -107x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-240 + -107x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(240 + 107x + 9x2) = 0

Factor a trinomial.
-1((80 + 9x)(3 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(80 + 9x)' equal to zero and attempt to solve:

Simplifying
80 + 9x = 0

Solving
80 + 9x = 0

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

Add '-80' to each side of the equation.
80 + -80 + 9x = 0 + -80

Combine like terms: 80 + -80 = 0
0 + 9x = 0 + -80
9x = 0 + -80

Combine like terms: 0 + -80 = -80
9x = -80

Divide each side by '9'.
x = -8.888888889

Simplifying
x = -8.888888889
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 = {-8.888888889, -3}