4z(z+15)=-144

Solution for 4z(z+15)=-144 equation:

Simplifying
4z(z + 15) = -144

Reorder the terms:
4z(15 + z) = -144
(15 * 4z + z * 4z) = -144
(60z + 4z2) = -144

Solving
60z + 4z2 = -144

Solving for variable 'z'.

Reorder the terms:
144 + 60z + 4z2 = -144 + 144

Combine like terms: -144 + 144 = 0
144 + 60z + 4z2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(36 + 15z + z2) = 0

Factor a trinomial.
4((12 + z)(3 + z)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(12 + z)' equal to zero and attempt to solve:

Simplifying
12 + z = 0

Solving
12 + z = 0

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

Add '-12' to each side of the equation.
12 + -12 + z = 0 + -12

Combine like terms: 12 + -12 = 0
0 + z = 0 + -12
z = 0 + -12

Combine like terms: 0 + -12 = -12
z = -12

Simplifying
z = -12
Subproblem 2
Set the factor '(3 + z)' equal to zero and attempt to solve:

Simplifying
3 + z = 0

Solving
3 + z = 0

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

Add '-3' to each side of the equation.
3 + -3 + z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + z = 0 + -3
z = 0 + -3

Combine like terms: 0 + -3 = -3
z = -3

Simplifying
z = -3
Solution
z = {-12, -3}