(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 = -10
-10 + -3x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-10 + -3x + x2 = 0

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

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-2, 5}