3z^2+6z=45

Solution for 3z^2+6z=45 equation:

Simplifying
3z2 + 6z = 45

Reorder the terms:
6z + 3z2 = 45

Solving
6z + 3z2 = 45

Solving for variable 'z'.

Reorder the terms:
-45 + 6z + 3z2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + 6z + 3z2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + 2z + z2) = 0

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

Ignore the factor 3.
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 '(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
Solution
z = {-5, 3}