(4g-9)(g+6)=0

Solution for (4g-9)(g+6)=0 equation:

Simplifying
(4g + -9)(g + 6) = 0

Reorder the terms:
(-9 + 4g)(g + 6) = 0

Reorder the terms:
(-9 + 4g)(6 + g) = 0

Multiply (-9 + 4g) * (6 + g)
(-9(6 + g) + 4g * (6 + g)) = 0
((6 * -9 + g * -9) + 4g * (6 + g)) = 0
((-54 + -9g) + 4g * (6 + g)) = 0
(-54 + -9g + (6 * 4g + g * 4g)) = 0
(-54 + -9g + (24g + 4g2)) = 0

Combine like terms: -9g + 24g = 15g
(-54 + 15g + 4g2) = 0

Solving
-54 + 15g + 4g2 = 0

Solving for variable 'g'.

Factor a trinomial.
(-6 + -1g)(9 + -4g) = 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 + -4g)' equal to zero and attempt to solve:

Simplifying
9 + -4g = 0

Solving
9 + -4g = 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 + -4g = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4g = 0 + -9
-4g = 0 + -9

Combine like terms: 0 + -9 = -9
-4g = -9

Divide each side by '-4'.
g = 2.25

Simplifying
g = 2.25
Solution
g = {-6, 2.25}