(3q-4)(2q+5)=0

Solution for (3q-4)(2q+5)=0 equation:

Simplifying
(3q + -4)(2q + 5) = 0

Reorder the terms:
(-4 + 3q)(2q + 5) = 0

Reorder the terms:
(-4 + 3q)(5 + 2q) = 0

Multiply (-4 + 3q) * (5 + 2q)
(-4(5 + 2q) + 3q * (5 + 2q)) = 0
((5 * -4 + 2q * -4) + 3q * (5 + 2q)) = 0
((-20 + -8q) + 3q * (5 + 2q)) = 0
(-20 + -8q + (5 * 3q + 2q * 3q)) = 0
(-20 + -8q + (15q + 6q2)) = 0

Combine like terms: -8q + 15q = 7q
(-20 + 7q + 6q2) = 0

Solving
-20 + 7q + 6q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(-5 + -2q)(4 + -3q) = 0

Subproblem 1
Set the factor '(-5 + -2q)' equal to zero and attempt to solve:

Simplifying
-5 + -2q = 0

Solving
-5 + -2q = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2q = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2q = 0 + 5
-2q = 0 + 5

Combine like terms: 0 + 5 = 5
-2q = 5

Divide each side by '-2'.
q = -2.5

Simplifying
q = -2.5
Subproblem 2
Set the factor '(4 + -3q)' equal to zero and attempt to solve:

Simplifying
4 + -3q = 0

Solving
4 + -3q = 0

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

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

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

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

Divide each side by '-3'.
q = 1.333333333

Simplifying
q = 1.333333333
Solution
q = {-2.5, 1.333333333}