15+4z=32z^2

Solution for 15+4z=32z^2 equation:

Simplifying
15 + 4z = 32z2

Solving
15 + 4z = 32z2

Solving for variable 'z'.

Combine like terms: 32z2 + -32z2 = 0
15 + 4z + -32z2 = 0

Factor a trinomial.
(3 + -4z)(5 + 8z) = 0

Subproblem 1
Set the factor '(3 + -4z)' equal to zero and attempt to solve:

Simplifying
3 + -4z = 0

Solving
3 + -4z = 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 + -4z = 0 + -3

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

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

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

Simplifying
z = 0.75
Subproblem 2
Set the factor '(5 + 8z)' equal to zero and attempt to solve:

Simplifying
5 + 8z = 0

Solving
5 + 8z = 0

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

Add '-5' to each side of the equation.
5 + -5 + 8z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 8z = 0 + -5
8z = 0 + -5

Combine like terms: 0 + -5 = -5
8z = -5

Divide each side by '8'.
z = -0.625

Simplifying
z = -0.625
Solution
z = {0.75, -0.625}