5z^2=90+15z

Solution for 5z^2=90+15z equation:

Simplifying
5z2 = 90 + 15z

Solving
5z2 = 90 + 15z

Solving for variable 'z'.

Reorder the terms:
-90 + -15z + 5z2 = 90 + 15z + -90 + -15z

Reorder the terms:
-90 + -15z + 5z2 = 90 + -90 + 15z + -15z

Combine like terms: 90 + -90 = 0
-90 + -15z + 5z2 = 0 + 15z + -15z
-90 + -15z + 5z2 = 15z + -15z

Combine like terms: 15z + -15z = 0
-90 + -15z + 5z2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-18 + -3z + z2) = 0

Factor a trinomial.
5((-3 + -1z)(6 + -1z)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-3 + -1z)' equal to zero and attempt to solve:

Simplifying
-3 + -1z = 0

Solving
-3 + -1z = 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 + -1z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1z = 0 + 3
-1z = 0 + 3

Combine like terms: 0 + 3 = 3
-1z = 3

Divide each side by '-1'.
z = -3

Simplifying
z = -3
Subproblem 2
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z = 0 + -6
-1z = 0 + -6

Combine like terms: 0 + -6 = -6
-1z = -6

Divide each side by '-1'.
z = 6

Simplifying
z = 6
Solution
z = {-3, 6}