4g^2+16gp+15p^2=0

Solution for 4g^2+16gp+15p^2=0 equation:

Simplifying
4g2 + 16gp + 15p2 = 0

Reorder the terms:
16gp + 4g2 + 15p2 = 0

Solving
16gp + 4g2 + 15p2 = 0

Solving for variable 'g'.

Factor a trinomial.
(2g + 3p)(2g + 5p) = 0

Subproblem 1
Set the factor '(2g + 3p)' equal to zero and attempt to solve:

Simplifying
2g + 3p = 0

Solving
2g + 3p = 0

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

Add '-3p' to each side of the equation.
2g + 3p + -3p = 0 + -3p

Combine like terms: 3p + -3p = 0
2g + 0 = 0 + -3p
2g = 0 + -3p
Remove the zero:
2g = -3p

Divide each side by '2'.
g = -1.5p

Simplifying
g = -1.5p
Subproblem 2
Set the factor '(2g + 5p)' equal to zero and attempt to solve:

Simplifying
2g + 5p = 0

Solving
2g + 5p = 0

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

Add '-5p' to each side of the equation.
2g + 5p + -5p = 0 + -5p

Combine like terms: 5p + -5p = 0
2g + 0 = 0 + -5p
2g = 0 + -5p
Remove the zero:
2g = -5p

Divide each side by '2'.
g = -2.5p

Simplifying
g = -2.5p
Solution
g = {-1.5p, -2.5p}