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

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

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

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

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

Multiply (-3 + 2a) * (-4 + a)
(-3(-4 + a) + 2a * (-4 + a)) = 18
((-4 * -3 + a * -3) + 2a * (-4 + a)) = 18
((12 + -3a) + 2a * (-4 + a)) = 18
(12 + -3a + (-4 * 2a + a * 2a)) = 18
(12 + -3a + (-8a + 2a2)) = 18

Combine like terms: -3a + -8a = -11a
(12 + -11a + 2a2) = 18

Solving
12 + -11a + 2a2 = 18

Solving for variable 'a'.

Reorder the terms:
12 + -18 + -11a + 2a2 = 18 + -18

Combine like terms: 12 + -18 = -6
-6 + -11a + 2a2 = 18 + -18

Combine like terms: 18 + -18 = 0
-6 + -11a + 2a2 = 0

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

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

Simplifying
-1 + -2a = 0

Solving
-1 + -2a = 0

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

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

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

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

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

Simplifying
a = -0.5
Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

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

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

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

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

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