(2x-3)(x-4)-18=0

Solution for (2x-3)(x-4)-18=0 equation:

Simplifying
(2x + -3)(x + -4) + -18 = 0

Reorder the terms:
(-3 + 2x)(x + -4) + -18 = 0

Reorder the terms:
(-3 + 2x)(-4 + x) + -18 = 0

Multiply (-3 + 2x) * (-4 + x)
(-3(-4 + x) + 2x * (-4 + x)) + -18 = 0
((-4 * -3 + x * -3) + 2x * (-4 + x)) + -18 = 0
((12 + -3x) + 2x * (-4 + x)) + -18 = 0
(12 + -3x + (-4 * 2x + x * 2x)) + -18 = 0
(12 + -3x + (-8x + 2x2)) + -18 = 0

Combine like terms: -3x + -8x = -11x
(12 + -11x + 2x2) + -18 = 0

Reorder the terms:
12 + -18 + -11x + 2x2 = 0

Combine like terms: 12 + -18 = -6
-6 + -11x + 2x2 = 0

Solving
-6 + -11x + 2x2 = 0

Solving for variable 'x'.

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

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 0

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

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

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

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

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

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

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

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

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

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

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

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