2g^2-14g=-20

Solution for 2g^2-14g=-20 equation:

Simplifying
2g2 + -14g = -20

Reorder the terms:
-14g + 2g2 = -20

Solving
-14g + 2g2 = -20

Solving for variable 'g'.

Reorder the terms:
20 + -14g + 2g2 = -20 + 20

Combine like terms: -20 + 20 = 0
20 + -14g + 2g2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -7g + g2) = 0

Factor a trinomial.
2((2 + -1g)(5 + -1g)) = 0

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

Simplifying
2 + -1g = 0

Solving
2 + -1g = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1g = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1g = 0 + -2
-1g = 0 + -2

Combine like terms: 0 + -2 = -2
-1g = -2

Divide each side by '-1'.
g = 2

Simplifying
g = 2
Subproblem 2
Set the factor '(5 + -1g)' equal to zero and attempt to solve:

Simplifying
5 + -1g = 0

Solving
5 + -1g = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1g = 0 + -5

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

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

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

Simplifying
g = 5
Solution
g = {2, 5}