(2q-3)(q+8)=0

Solution for (2q-3)(q+8)=0 equation:

Simplifying
(2q + -3)(q + 8) = 0

Reorder the terms:
(-3 + 2q)(q + 8) = 0

Reorder the terms:
(-3 + 2q)(8 + q) = 0

Multiply (-3 + 2q) * (8 + q)
(-3(8 + q) + 2q * (8 + q)) = 0
((8 * -3 + q * -3) + 2q * (8 + q)) = 0
((-24 + -3q) + 2q * (8 + q)) = 0
(-24 + -3q + (8 * 2q + q * 2q)) = 0
(-24 + -3q + (16q + 2q2)) = 0

Combine like terms: -3q + 16q = 13q
(-24 + 13q + 2q2) = 0

Solving
-24 + 13q + 2q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(-8 + -1q)(3 + -2q) = 0

Subproblem 1
Set the factor '(-8 + -1q)' equal to zero and attempt to solve:

Simplifying
-8 + -1q = 0

Solving
-8 + -1q = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1q = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1q = 0 + 8
-1q = 0 + 8

Combine like terms: 0 + 8 = 8
-1q = 8

Divide each side by '-1'.
q = -8

Simplifying
q = -8
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 = {-8, 1.5}