3z^2-4z=15

Solution for 3z^2-4z=15 equation:

Simplifying
3z2 + -4z = 15

Reorder the terms:
-4z + 3z2 = 15

Solving
-4z + 3z2 = 15

Solving for variable 'z'.

Reorder the terms:
-15 + -4z + 3z2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -4z + 3z2 = 0

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

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

Simplifying
-5 + -3z = 0

Solving
-5 + -3z = 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 + -3z = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3z = 0 + 5
-3z = 0 + 5

Combine like terms: 0 + 5 = 5
-3z = 5

Divide each side by '-3'.
z = -1.666666667

Simplifying
z = -1.666666667
Subproblem 2
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
Solution
z = {-1.666666667, 3}