-10z^2=11z-6

Solution for -10z^2=11z-6 equation:

Simplifying
-10z2 = 11z + -6

Reorder the terms:
-10z2 = -6 + 11z

Solving
-10z2 = -6 + 11z

Solving for variable 'z'.

Reorder the terms:
6 + -11z + -10z2 = -6 + 11z + 6 + -11z

Reorder the terms:
6 + -11z + -10z2 = -6 + 6 + 11z + -11z

Combine like terms: -6 + 6 = 0
6 + -11z + -10z2 = 0 + 11z + -11z
6 + -11z + -10z2 = 11z + -11z

Combine like terms: 11z + -11z = 0
6 + -11z + -10z2 = 0

Factor a trinomial.
(2 + -5z)(3 + 2z) = 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 + 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
Solution
z = {0.4, -1.5}