5z^2=6-13z

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

Simplifying
5z2 = 6 + -13z

Solving
5z2 = 6 + -13z

Solving for variable 'z'.

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

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

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

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

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

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

Simplifying
-3 + -1z = 0

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

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

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

Divide each side by '-1'.
z = -3

Simplifying
z = -3
Subproblem 2
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
Solution
z = {-3, 0.4}