(x+1)(x-4)-6=0

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Solution for (x+1)(x-4)-6=0 equation: 


Simplifying
(x + 1)(x + -4) + -6 = 0

Reorder the terms:
(1 + x)(x + -4) + -6 = 0

Reorder the terms:
(1 + x)(-4 + x) + -6 = 0

Multiply (1 + x) * (-4 + x)
(1(-4 + x) + x(-4 + x)) + -6 = 0
((-4 * 1 + x * 1) + x(-4 + x)) + -6 = 0
((-4 + 1x) + x(-4 + x)) + -6 = 0
(-4 + 1x + (-4 * x + x * x)) + -6 = 0
(-4 + 1x + (-4x + x2)) + -6 = 0

Combine like terms: 1x + -4x = -3x
(-4 + -3x + x2) + -6 = 0

Reorder the terms:
-4 + -6 + -3x + x2 = 0

Combine like terms: -4 + -6 = -10
-10 + -3x + x2 = 0

Solving
-10 + -3x + x2 = 0

Solving for variable 'x'.

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}

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