(g+17)(g-2)-20=0

Solution for (g+17)(g-2)-20=0 equation:

Simplifying
(g + 17)(g + -2) + -20 = 0

Reorder the terms:
(17 + g)(g + -2) + -20 = 0

Reorder the terms:
(17 + g)(-2 + g) + -20 = 0

Multiply (17 + g) * (-2 + g)
(17(-2 + g) + g(-2 + g)) + -20 = 0
((-2 * 17 + g * 17) + g(-2 + g)) + -20 = 0
((-34 + 17g) + g(-2 + g)) + -20 = 0
(-34 + 17g + (-2 * g + g * g)) + -20 = 0
(-34 + 17g + (-2g + g2)) + -20 = 0

Combine like terms: 17g + -2g = 15g
(-34 + 15g + g2) + -20 = 0

Reorder the terms:
-34 + -20 + 15g + g2 = 0

Combine like terms: -34 + -20 = -54
-54 + 15g + g2 = 0

Solving
-54 + 15g + g2 = 0

Solving for variable 'g'.

Factor a trinomial.
(-18 + -1g)(3 + -1g) = 0

Subproblem 1
Set the factor '(-18 + -1g)' equal to zero and attempt to solve:

Simplifying
-18 + -1g = 0

Solving
-18 + -1g = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1g = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1g = 0 + 18
-1g = 0 + 18

Combine like terms: 0 + 18 = 18
-1g = 18

Divide each side by '-1'.
g = -18

Simplifying
g = -18
Subproblem 2
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
Solution
g = {-18, 3}