5z(4z-3)=-8z+6

Solution for 5z(4z-3)=-8z+6 equation:

Simplifying
5z(4z + -3) = -8z + 6

Reorder the terms:
5z(-3 + 4z) = -8z + 6
(-3 * 5z + 4z * 5z) = -8z + 6
(-15z + 20z2) = -8z + 6

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

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

Solving for variable 'z'.

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

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

Reorder the terms:
-6 + -7z + 20z2 = 6 + -6 + -8z + 8z

Combine like terms: 6 + -6 = 0
-6 + -7z + 20z2 = 0 + -8z + 8z
-6 + -7z + 20z2 = -8z + 8z

Combine like terms: -8z + 8z = 0
-6 + -7z + 20z2 = 0

Factor a trinomial.
(-2 + -5z)(3 + -4z) = 0

Subproblem 1
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
Subproblem 2
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
Solution
z = {-0.4, 0.75}