-10z^2+11z=3

Solution for -10z^2+11z=3 equation:

Simplifying
-10z2 + 11z = 3

Reorder the terms:
11z + -10z2 = 3

Solving
11z + -10z2 = 3

Solving for variable 'z'.

Reorder the terms:
-3 + 11z + -10z2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 11z + -10z2 = 0

Factor a trinomial.
(-3 + 5z)(1 + -2z) = 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 '(1 + -2z)' equal to zero and attempt to solve:

Simplifying
1 + -2z = 0

Solving
1 + -2z = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2z = 0 + -1
-2z = 0 + -1

Combine like terms: 0 + -1 = -1
-2z = -1

Divide each side by '-2'.
z = 0.5

Simplifying
z = 0.5
Solution
z = {0.6, 0.5}