g^2-22g-75=0

Solution for g^2-22g-75=0 equation:

Simplifying
g2 + -22g + -75 = 0

Reorder the terms:
-75 + -22g + g2 = 0

Solving
-75 + -22g + g2 = 0

Solving for variable 'g'.

Factor a trinomial.
(-3 + -1g)(25 + -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 '(25 + -1g)' equal to zero and attempt to solve:

Simplifying
25 + -1g = 0

Solving
25 + -1g = 0

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

Add '-25' to each side of the equation.
25 + -25 + -1g = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -1g = 0 + -25
-1g = 0 + -25

Combine like terms: 0 + -25 = -25
-1g = -25

Divide each side by '-1'.
g = 25

Simplifying
g = 25
Solution
g = {-3, 25}