15z^2-20z+6=-z

Solution for 15z^2-20z+6=-z equation:

Simplifying
15z2 + -20z + 6 = -1z

Reorder the terms:
6 + -20z + 15z2 = -1z

Solving
6 + -20z + 15z2 = -1z

Solving for variable 'z'.

Reorder the terms:
6 + -20z + z + 15z2 = -1z + z

Combine like terms: -20z + z = -19z
6 + -19z + 15z2 = -1z + z

Combine like terms: -1z + z = 0
6 + -19z + 15z2 = 0

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

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

Simplifying
3 + -5z = 0

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

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

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

Divide each side by '-5'.
z = 0.6

Simplifying
z = 0.6
Subproblem 2
Set the factor '(2 + -3z)' equal to zero and attempt to solve:

Simplifying
2 + -3z = 0

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

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

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

Divide each side by '-3'.
z = 0.6666666667

Simplifying
z = 0.6666666667
Solution
z = {0.6, 0.6666666667}