(2x-1)(x-4)=22

Solution for (2x-1)(x-4)=22 equation:

Simplifying
(2x + -1)(x + -4) = 22

Reorder the terms:
(-1 + 2x)(x + -4) = 22

Reorder the terms:
(-1 + 2x)(-4 + x) = 22

Multiply (-1 + 2x) * (-4 + x)
(-1(-4 + x) + 2x * (-4 + x)) = 22
((-4 * -1 + x * -1) + 2x * (-4 + x)) = 22
((4 + -1x) + 2x * (-4 + x)) = 22
(4 + -1x + (-4 * 2x + x * 2x)) = 22
(4 + -1x + (-8x + 2x2)) = 22

Combine like terms: -1x + -8x = -9x
(4 + -9x + 2x2) = 22

Solving
4 + -9x + 2x2 = 22

Solving for variable 'x'.

Reorder the terms:
4 + -22 + -9x + 2x2 = 22 + -22

Combine like terms: 4 + -22 = -18
-18 + -9x + 2x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-18 + -9x + 2x2 = 0

Factor a trinomial.
(-3 + -2x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5
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 = {-1.5, 6}