10=z^2+3z

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

Simplifying
10 = z2 + 3z

Reorder the terms:
10 = 3z + z2

Solving
10 = 3z + z2

Solving for variable 'z'.

Reorder the terms:
10 + -3z + -1z2 = 3z + -3z + z2 + -1z2

Combine like terms: 3z + -3z = 0
10 + -3z + -1z2 = 0 + z2 + -1z2
10 + -3z + -1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
10 + -3z + -1z2 = 0

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

Subproblem 1
Set the factor '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

Solving
2 + -1z = 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 + -1z = 0 + -2

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

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

Divide each side by '-1'.
z = 2

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

Simplifying
5 + z = 0

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

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

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

Simplifying
z = -5
Solution
z = {2, -5}