(2x-1)(x+4)=26

Solution for (2x-1)(x+4)=26 equation:

Simplifying
(2x + -1)(x + 4) = 26

Reorder the terms:
(-1 + 2x)(x + 4) = 26

Reorder the terms:
(-1 + 2x)(4 + x) = 26

Multiply (-1 + 2x) * (4 + x)
(-1(4 + x) + 2x * (4 + x)) = 26
((4 * -1 + x * -1) + 2x * (4 + x)) = 26
((-4 + -1x) + 2x * (4 + x)) = 26
(-4 + -1x + (4 * 2x + x * 2x)) = 26
(-4 + -1x + (8x + 2x2)) = 26

Combine like terms: -1x + 8x = 7x
(-4 + 7x + 2x2) = 26

Solving
-4 + 7x + 2x2 = 26

Solving for variable 'x'.

Reorder the terms:
-4 + -26 + 7x + 2x2 = 26 + -26

Combine like terms: -4 + -26 = -30
-30 + 7x + 2x2 = 26 + -26

Combine like terms: 26 + -26 = 0
-30 + 7x + 2x2 = 0

Factor a trinomial.
(-6 + -1x)(5 + -2x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {-6, 2.5}