2z^2+z-36=0

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

Simplifying
2z2 + z + -36 = 0

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

Solving
-36 + z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-9 + -2z)(4 + -1z) = 0

Subproblem 1
Set the factor '(-9 + -2z)' equal to zero and attempt to solve:

Simplifying
-9 + -2z = 0

Solving
-9 + -2z = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2z = 0 + 9

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

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

Divide each side by '-2'.
z = -4.5

Simplifying
z = -4.5
Subproblem 2
Set the factor '(4 + -1z)' equal to zero and attempt to solve:

Simplifying
4 + -1z = 0

Solving
4 + -1z = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1z = 0 + -4
-1z = 0 + -4

Combine like terms: 0 + -4 = -4
-1z = -4

Divide each side by '-1'.
z = 4

Simplifying
z = 4
Solution
z = {-4.5, 4}