14x^2+64x-120=0

Solution for 14x^2+64x-120=0 equation:

Simplifying
14x2 + 64x + -120 = 0

Reorder the terms:
-120 + 64x + 14x2 = 0

Solving
-120 + 64x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-60 + 32x + 7x2) = 0

Factor a trinomial.
2((-6 + -1x)(10 + -7x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 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 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(10 + -7x)' equal to zero and attempt to solve:

Simplifying
10 + -7x = 0

Solving
10 + -7x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -7x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -7x = 0 + -10
-7x = 0 + -10

Combine like terms: 0 + -10 = -10
-7x = -10

Divide each side by '-7'.
x = 1.428571429

Simplifying
x = 1.428571429
Solution
x = {-6, 1.428571429}