(x+4)(x-1)=-6

Solution for (x+4)(x-1)=-6 equation:

Simplifying
(x + 4)(x + -1) = -6

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

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

Multiply (4 + x) * (-1 + x)
(4(-1 + x) + x(-1 + x)) = -6
((-1 * 4 + x * 4) + x(-1 + x)) = -6
((-4 + 4x) + x(-1 + x)) = -6
(-4 + 4x + (-1 * x + x * x)) = -6
(-4 + 4x + (-1x + x2)) = -6

Combine like terms: 4x + -1x = 3x
(-4 + 3x + x2) = -6

Solving
-4 + 3x + x2 = -6

Solving for variable 'x'.

Reorder the terms:
-4 + 6 + 3x + x2 = -6 + 6

Combine like terms: -4 + 6 = 2
2 + 3x + x2 = -6 + 6

Combine like terms: -6 + 6 = 0
2 + 3x + x2 = 0

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

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {-2, -1}