4z(z-1)=15

Solution for 4z(z-1)=15 equation:

Simplifying
4z(z + -1) = 15

Reorder the terms:
4z(-1 + z) = 15
(-1 * 4z + z * 4z) = 15
(-4z + 4z2) = 15

Solving
-4z + 4z2 = 15

Solving for variable 'z'.

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

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

Factor a trinomial.
(-3 + -2z)(5 + -2z) = 0

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

Simplifying
-3 + -2z = 0

Solving
-3 + -2z = 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 + -2z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2z = 0 + 3
-2z = 0 + 3

Combine like terms: 0 + 3 = 3
-2z = 3

Divide each side by '-2'.
z = -1.5

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

Simplifying
5 + -2z = 0

Solving
5 + -2z = 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 + -2z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2z = 0 + -5
-2z = 0 + -5

Combine like terms: 0 + -5 = -5
-2z = -5

Divide each side by '-2'.
z = 2.5

Simplifying
z = 2.5
Solution
z = {-1.5, 2.5}