3z^2+13z=10

Solution for 3z^2+13z=10 equation:

Simplifying
3z2 + 13z = 10

Reorder the terms:
13z + 3z2 = 10

Solving
13z + 3z2 = 10

Solving for variable 'z'.

Reorder the terms:
-10 + 13z + 3z2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 13z + 3z2 = 0

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

Subproblem 1
Set the factor '(-5 + -1z)' equal to zero and attempt to solve:

Simplifying
-5 + -1z = 0

Solving
-5 + -1z = 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 + -1z = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1z = 0 + 5
-1z = 0 + 5

Combine like terms: 0 + 5 = 5
-1z = 5

Divide each side by '-1'.
z = -5

Simplifying
z = -5
Subproblem 2
Set the factor '(2 + -3z)' equal to zero and attempt to solve:

Simplifying
2 + -3z = 0

Solving
2 + -3z = 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 + -3z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3z = 0 + -2
-3z = 0 + -2

Combine like terms: 0 + -2 = -2
-3z = -2

Divide each side by '-3'.
z = 0.6666666667

Simplifying
z = 0.6666666667
Solution
z = {-5, 0.6666666667}