(2x-1)(x-4)=39

Solution for (2x-1)(x-4)=39 equation:

Simplifying
(2x + -1)(x + -4) = 39

Reorder the terms:
(-1 + 2x)(x + -4) = 39

Reorder the terms:
(-1 + 2x)(-4 + x) = 39

Multiply (-1 + 2x) * (-4 + x)
(-1(-4 + x) + 2x * (-4 + x)) = 39
((-4 * -1 + x * -1) + 2x * (-4 + x)) = 39
((4 + -1x) + 2x * (-4 + x)) = 39
(4 + -1x + (-4 * 2x + x * 2x)) = 39
(4 + -1x + (-8x + 2x2)) = 39

Combine like terms: -1x + -8x = -9x
(4 + -9x + 2x2) = 39

Solving
4 + -9x + 2x2 = 39

Solving for variable 'x'.

Reorder the terms:
4 + -39 + -9x + 2x2 = 39 + -39

Combine like terms: 4 + -39 = -35
-35 + -9x + 2x2 = 39 + -39

Combine like terms: 39 + -39 = 0
-35 + -9x + 2x2 = 0

Factor a trinomial.
(-5 + -2x)(7 + -1x) = 0

Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-2.5, 7}