(2x-1)(x+6)=24

Solution for (2x-1)(x+6)=24 equation:

Simplifying
(2x + -1)(x + 6) = 24

Reorder the terms:
(-1 + 2x)(x + 6) = 24

Reorder the terms:
(-1 + 2x)(6 + x) = 24

Multiply (-1 + 2x) * (6 + x)
(-1(6 + x) + 2x * (6 + x)) = 24
((6 * -1 + x * -1) + 2x * (6 + x)) = 24
((-6 + -1x) + 2x * (6 + x)) = 24
(-6 + -1x + (6 * 2x + x * 2x)) = 24
(-6 + -1x + (12x + 2x2)) = 24

Combine like terms: -1x + 12x = 11x
(-6 + 11x + 2x2) = 24

Solving
-6 + 11x + 2x2 = 24

Solving for variable 'x'.

Reorder the terms:
-6 + -24 + 11x + 2x2 = 24 + -24

Combine like terms: -6 + -24 = -30
-30 + 11x + 2x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-30 + 11x + 2x2 = 0

Factor a trinomial.
(-15 + -2x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-15 + -2x)' equal to zero and attempt to solve:

Simplifying
-15 + -2x = 0

Solving
-15 + -2x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -2x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -2x = 0 + 15
-2x = 0 + 15

Combine like terms: 0 + 15 = 15
-2x = 15

Divide each side by '-2'.
x = -7.5

Simplifying
x = -7.5
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-7.5, 2}