13z+5=6z^2

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

Simplifying
13z + 5 = 6z2

Reorder the terms:
5 + 13z = 6z2

Solving
5 + 13z = 6z2

Solving for variable 'z'.

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

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

Subproblem 1
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
Subproblem 2
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
Solution
z = {2.5, -0.3333333333}