9z+45=2z^2

Solution for 9z+45=2z^2 equation:

Simplifying
9z + 45 = 2z2

Reorder the terms:
45 + 9z = 2z2

Solving
45 + 9z = 2z2

Solving for variable 'z'.

Combine like terms: 2z2 + -2z2 = 0
45 + 9z + -2z2 = 0

Factor a trinomial.
(15 + -2z)(3 + z) = 0

Subproblem 1
Set the factor '(15 + -2z)' equal to zero and attempt to solve:

Simplifying
15 + -2z = 0

Solving
15 + -2z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-15' to each side of the equation.
15 + -15 + -2z = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -2z = 0 + -15
-2z = 0 + -15

Combine like terms: 0 + -15 = -15
-2z = -15

Divide each side by '-2'.
z = 7.5

Simplifying
z = 7.5
Subproblem 2
Set the factor '(3 + z)' equal to zero and attempt to solve:

Simplifying
3 + z = 0

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

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

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

Simplifying
z = -3
Solution
z = {7.5, -3}