2z^2+21z-36=0

Solution for 2z^2+21z-36=0 equation:

Simplifying
2z2 + 21z + -36 = 0

Reorder the terms:
-36 + 21z + 2z2 = 0

Solving
-36 + 21z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-12 + -1z)(3 + -2z) = 0

Subproblem 1
Set the factor '(-12 + -1z)' equal to zero and attempt to solve:

Simplifying
-12 + -1z = 0

Solving
-12 + -1z = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1z = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1z = 0 + 12
-1z = 0 + 12

Combine like terms: 0 + 12 = 12
-1z = 12

Divide each side by '-1'.
z = -12

Simplifying
z = -12
Subproblem 2
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
Solution
z = {-12, 1.5}