36z^2+78z=-36

Solution for 36z^2+78z=-36 equation:

Simplifying
36z2 + 78z = -36

Reorder the terms:
78z + 36z2 = -36

Solving
78z + 36z2 = -36

Solving for variable 'z'.

Reorder the terms:
36 + 78z + 36z2 = -36 + 36

Combine like terms: -36 + 36 = 0
36 + 78z + 36z2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(6 + 13z + 6z2) = 0

Factor a trinomial.
6((3 + 2z)(2 + 3z)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(3 + 2z)' equal to zero and attempt to solve:

Simplifying
3 + 2z = 0

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

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

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

Divide each side by '2'.
z = -1.5

Simplifying
z = -1.5
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 = {-1.5, -0.6666666667}