(4q-6)(4q+3)=0

Solution for (4q-6)(4q+3)=0 equation:

Simplifying
(4q + -6)(4q + 3) = 0

Reorder the terms:
(-6 + 4q)(4q + 3) = 0

Reorder the terms:
(-6 + 4q)(3 + 4q) = 0

Multiply (-6 + 4q) * (3 + 4q)
(-6(3 + 4q) + 4q * (3 + 4q)) = 0
((3 * -6 + 4q * -6) + 4q * (3 + 4q)) = 0
((-18 + -24q) + 4q * (3 + 4q)) = 0
(-18 + -24q + (3 * 4q + 4q * 4q)) = 0
(-18 + -24q + (12q + 16q2)) = 0

Combine like terms: -24q + 12q = -12q
(-18 + -12q + 16q2) = 0

Solving
-18 + -12q + 16q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -6q + 8q2) = 0

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

Ignore the factor 2.
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 '(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 = {-0.75, 1.5}