6z^2-19z=-10

Solution for 6z^2-19z=-10 equation:

Simplifying
6z2 + -19z = -10

Reorder the terms:
-19z + 6z2 = -10

Solving
-19z + 6z2 = -10

Solving for variable 'z'.

Reorder the terms:
10 + -19z + 6z2 = -10 + 10

Combine like terms: -10 + 10 = 0
10 + -19z + 6z2 = 0

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

Subproblem 1
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
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 = {0.6666666667, 2.5}