40q^2-40q-30=0

Solution for 40q^2-40q-30=0 equation:

Simplifying
40q2 + -40q + -30 = 0

Reorder the terms:
-30 + -40q + 40q2 = 0

Solving
-30 + -40q + 40q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-3 + -4q + 4q2) = 0

Factor a trinomial.
10((-1 + -2q)(3 + -2q)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-1 + -2q)' equal to zero and attempt to solve:

Simplifying
-1 + -2q = 0

Solving
-1 + -2q = 0

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

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

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

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

Divide each side by '-2'.
q = -0.5

Simplifying
q = -0.5
Subproblem 2
Set the factor '(3 + -2q)' equal to zero and attempt to solve:

Simplifying
3 + -2q = 0

Solving
3 + -2q = 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 + -2q = 0 + -3

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

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

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

Simplifying
q = 1.5
Solution
q = {-0.5, 1.5}