6z^2-5=13z

Solution for 6z^2-5=13z equation:

Simplifying
6z2 + -5 = 13z

Reorder the terms:
-5 + 6z2 = 13z

Solving
-5 + 6z2 = 13z

Solving for variable 'z'.

Reorder the terms:
-5 + -13z + 6z2 = 13z + -13z

Combine like terms: 13z + -13z = 0
-5 + -13z + 6z2 = 0

Factor a trinomial.
(-1 + -3z)(5 + -2z) = 0

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

Simplifying
-1 + -3z = 0

Solving
-1 + -3z = 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 + -3z = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3z = 0 + 1
-3z = 0 + 1

Combine like terms: 0 + 1 = 1
-3z = 1

Divide each side by '-3'.
z = -0.3333333333

Simplifying
z = -0.3333333333
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 = {-0.3333333333, 2.5}