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

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

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

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

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

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

Combine like terms: -1x + 4x = 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.
(-5 + -1x)(2 + -1x) = 0

Subproblem 1
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
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 = {-5, 2}