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

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

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

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

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

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

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

Solving
-4 + 3x + x2 = 24

Solving for variable 'x'.

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

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

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

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}