g^2-3g-54=0

Solution for g^2-3g-54=0 equation:

Simplifying
g2 + -3g + -54 = 0

Reorder the terms:
-54 + -3g + g2 = 0

Solving
-54 + -3g + g2 = 0

Solving for variable 'g'.

Factor a trinomial.
(-6 + -1g)(9 + -1g) = 0

Subproblem 1
Set the factor '(-6 + -1g)' equal to zero and attempt to solve:

Simplifying
-6 + -1g = 0

Solving
-6 + -1g = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1g = 0 + 6

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

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

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

Simplifying
g = -6
Subproblem 2
Set the factor '(9 + -1g)' equal to zero and attempt to solve:

Simplifying
9 + -1g = 0

Solving
9 + -1g = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1g = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1g = 0 + -9
-1g = 0 + -9

Combine like terms: 0 + -9 = -9
-1g = -9

Divide each side by '-1'.
g = 9

Simplifying
g = 9
Solution
g = {-6, 9}