4g(g+6)=g-15

Solution for 4g(g+6)=g-15 equation:

Simplifying
4g(g + 6) = g + -15

Reorder the terms:
4g(6 + g) = g + -15
(6 * 4g + g * 4g) = g + -15
(24g + 4g2) = g + -15

Reorder the terms:
24g + 4g2 = -15 + g

Solving
24g + 4g2 = -15 + g

Solving for variable 'g'.

Reorder the terms:
15 + 24g + -1g + 4g2 = -15 + g + 15 + -1g

Combine like terms: 24g + -1g = 23g
15 + 23g + 4g2 = -15 + g + 15 + -1g

Reorder the terms:
15 + 23g + 4g2 = -15 + 15 + g + -1g

Combine like terms: -15 + 15 = 0
15 + 23g + 4g2 = 0 + g + -1g
15 + 23g + 4g2 = g + -1g

Combine like terms: g + -1g = 0
15 + 23g + 4g2 = 0

Factor a trinomial.
(5 + g)(3 + 4g) = 0

Subproblem 1
Set the factor '(5 + g)' equal to zero and attempt to solve:

Simplifying
5 + g = 0

Solving
5 + g = 0

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

Add '-5' to each side of the equation.
5 + -5 + g = 0 + -5

Combine like terms: 5 + -5 = 0
0 + g = 0 + -5
g = 0 + -5

Combine like terms: 0 + -5 = -5
g = -5

Simplifying
g = -5
Subproblem 2
Set the factor '(3 + 4g)' equal to zero and attempt to solve:

Simplifying
3 + 4g = 0

Solving
3 + 4g = 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 + 4g = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4g = 0 + -3
4g = 0 + -3

Combine like terms: 0 + -3 = -3
4g = -3

Divide each side by '4'.
g = -0.75

Simplifying
g = -0.75
Solution
g = {-5, -0.75}