(x-1)(x+4)-24=0

Solution for (x-1)(x+4)-24=0 equation:

Simplifying
(x + -1)(x + 4) + -24 = 0

Reorder the terms:
(-1 + x)(x + 4) + -24 = 0

Reorder the terms:
(-1 + x)(4 + x) + -24 = 0

Multiply (-1 + x) * (4 + x)
(-1(4 + x) + x(4 + x)) + -24 = 0
((4 * -1 + x * -1) + x(4 + x)) + -24 = 0
((-4 + -1x) + x(4 + x)) + -24 = 0
(-4 + -1x + (4 * x + x * x)) + -24 = 0
(-4 + -1x + (4x + x2)) + -24 = 0

Combine like terms: -1x + 4x = 3x
(-4 + 3x + x2) + -24 = 0

Reorder the terms:
-4 + -24 + 3x + x2 = 0

Combine like terms: -4 + -24 = -28
-28 + 3x + x2 = 0

Solving
-28 + 3x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -1x)(4 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-7, 4}