4z(5z-2)=-15z+6

Solution for 4z(5z-2)=-15z+6 equation:

Simplifying
4z(5z + -2) = -15z + 6

Reorder the terms:
4z(-2 + 5z) = -15z + 6
(-2 * 4z + 5z * 4z) = -15z + 6
(-8z + 20z2) = -15z + 6

Reorder the terms:
-8z + 20z2 = 6 + -15z

Solving
-8z + 20z2 = 6 + -15z

Solving for variable 'z'.

Reorder the terms:
-6 + -8z + 15z + 20z2 = 6 + -15z + -6 + 15z

Combine like terms: -8z + 15z = 7z
-6 + 7z + 20z2 = 6 + -15z + -6 + 15z

Reorder the terms:
-6 + 7z + 20z2 = 6 + -6 + -15z + 15z

Combine like terms: 6 + -6 = 0
-6 + 7z + 20z2 = 0 + -15z + 15z
-6 + 7z + 20z2 = -15z + 15z

Combine like terms: -15z + 15z = 0
-6 + 7z + 20z2 = 0

Factor a trinomial.
(-3 + -4z)(2 + -5z) = 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 '(2 + -5z)' equal to zero and attempt to solve:

Simplifying
2 + -5z = 0

Solving
2 + -5z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5z = 0 + -2

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

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

Divide each side by '-5'.
z = 0.4

Simplifying
z = 0.4
Solution
z = {-0.75, 0.4}