(2q-3)(q-4)=18

Solution for (2q-3)(q-4)=18 equation:

Simplifying
(2q + -3)(q + -4) = 18

Reorder the terms:
(-3 + 2q)(q + -4) = 18

Reorder the terms:
(-3 + 2q)(-4 + q) = 18

Multiply (-3 + 2q) * (-4 + q)
(-3(-4 + q) + 2q * (-4 + q)) = 18
((-4 * -3 + q * -3) + 2q * (-4 + q)) = 18
((12 + -3q) + 2q * (-4 + q)) = 18
(12 + -3q + (-4 * 2q + q * 2q)) = 18
(12 + -3q + (-8q + 2q2)) = 18

Combine like terms: -3q + -8q = -11q
(12 + -11q + 2q2) = 18

Solving
12 + -11q + 2q2 = 18

Solving for variable 'q'.

Reorder the terms:
12 + -18 + -11q + 2q2 = 18 + -18

Combine like terms: 12 + -18 = -6
-6 + -11q + 2q2 = 18 + -18

Combine like terms: 18 + -18 = 0
-6 + -11q + 2q2 = 0

Factor a trinomial.
(-1 + -2q)(6 + -1q) = 0

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 '(6 + -1q)' equal to zero and attempt to solve:

Simplifying
6 + -1q = 0

Solving
6 + -1q = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1q = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1q = 0 + -6
-1q = 0 + -6

Combine like terms: 0 + -6 = -6
-1q = -6

Divide each side by '-1'.
q = 6

Simplifying
q = 6
Solution
q = {-0.5, 6}