4q^2-5q-6=0

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

Simplifying
4q2 + -5q + -6 = 0

Reorder the terms:
-6 + -5q + 4q2 = 0

Solving
-6 + -5q + 4q2 = 0

Solving for variable 'q'.

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

Subproblem 1
Set the factor '(-3 + -4q)' equal to zero and attempt to solve:

Simplifying
-3 + -4q = 0

Solving
-3 + -4q = 0

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

Add '3' to each side of the equation.
-3 + 3 + -4q = 0 + 3

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

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

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

Simplifying
q = -0.75
Subproblem 2
Set the factor '(2 + -1q)' equal to zero and attempt to solve:

Simplifying
2 + -1q = 0

Solving
2 + -1q = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1q = 0 + -2

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

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

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

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