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

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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.
(-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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