4z^2+5z-6=0

Solution for 4z^2+5z-6=0 equation:

Simplifying
4z2 + 5z + -6 = 0

Reorder the terms:
-6 + 5z + 4z2 = 0

Solving
-6 + 5z + 4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-2 + -1z)(3 + -4z) = 0

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

Simplifying
-2 + -1z = 0

Solving
-2 + -1z = 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 + -1z = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1z = 0 + 2
-1z = 0 + 2

Combine like terms: 0 + 2 = 2
-1z = 2

Divide each side by '-1'.
z = -2

Simplifying
z = -2
Subproblem 2
Set the factor '(3 + -4z)' equal to zero and attempt to solve:

Simplifying
3 + -4z = 0

Solving
3 + -4z = 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 + -4z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4z = 0 + -3
-4z = 0 + -3

Combine like terms: 0 + -3 = -3
-4z = -3

Divide each side by '-4'.
z = 0.75

Simplifying
z = 0.75
Solution
z = {-2, 0.75}