g^2-14g=51

Solution for g^2-14g=51 equation:

Simplifying
g2 + -14g = 51

Reorder the terms:
-14g + g2 = 51

Solving
-14g + g2 = 51

Solving for variable 'g'.

Reorder the terms:
-51 + -14g + g2 = 51 + -51

Combine like terms: 51 + -51 = 0
-51 + -14g + g2 = 0

Factor a trinomial.
(-3 + -1g)(17 + -1g) = 0

Subproblem 1
Set the factor '(-3 + -1g)' equal to zero and attempt to solve:

Simplifying
-3 + -1g = 0

Solving
-3 + -1g = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1g = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1g = 0 + 3
-1g = 0 + 3

Combine like terms: 0 + 3 = 3
-1g = 3

Divide each side by '-1'.
g = -3

Simplifying
g = -3
Subproblem 2
Set the factor '(17 + -1g)' equal to zero and attempt to solve:

Simplifying
17 + -1g = 0

Solving
17 + -1g = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1g = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1g = 0 + -17
-1g = 0 + -17

Combine like terms: 0 + -17 = -17
-1g = -17

Divide each side by '-1'.
g = 17

Simplifying
g = 17
Solution
g = {-3, 17}