3(X+2)(X-4)=(X+2)(X+1)

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Solution for 3(X+2)(X-4)=(X+2)(X+1) equation: 


Simplifying
3(X + 2)(X + -4) = (X + 2)(X + 1)

Reorder the terms:
3(2 + X)(X + -4) = (X + 2)(X + 1)

Reorder the terms:
3(2 + X)(-4 + X) = (X + 2)(X + 1)

Multiply (2 + X) * (-4 + X)
3(2(-4 + X) + X(-4 + X)) = (X + 2)(X + 1)
3((-4 * 2 + X * 2) + X(-4 + X)) = (X + 2)(X + 1)
3((-8 + 2X) + X(-4 + X)) = (X + 2)(X + 1)
3(-8 + 2X + (-4 * X + X * X)) = (X + 2)(X + 1)
3(-8 + 2X + (-4X + X2)) = (X + 2)(X + 1)

Combine like terms: 2X + -4X = -2X
3(-8 + -2X + X2) = (X + 2)(X + 1)
(-8 * 3 + -2X * 3 + X2 * 3) = (X + 2)(X + 1)
(-24 + -6X + 3X2) = (X + 2)(X + 1)

Reorder the terms:
-24 + -6X + 3X2 = (2 + X)(X + 1)

Reorder the terms:
-24 + -6X + 3X2 = (2 + X)(1 + X)

Multiply (2 + X) * (1 + X)
-24 + -6X + 3X2 = (2(1 + X) + X(1 + X))
-24 + -6X + 3X2 = ((1 * 2 + X * 2) + X(1 + X))
-24 + -6X + 3X2 = ((2 + 2X) + X(1 + X))
-24 + -6X + 3X2 = (2 + 2X + (1 * X + X * X))
-24 + -6X + 3X2 = (2 + 2X + (1X + X2))

Combine like terms: 2X + 1X = 3X
-24 + -6X + 3X2 = (2 + 3X + X2)

Solving
-24 + -6X + 3X2 = 2 + 3X + X2

Solving for variable 'X'.

Reorder the terms:
-24 + -2 + -6X + -3X + 3X2 + -1X2 = 2 + 3X + X2 + -2 + -3X + -1X2

Combine like terms: -24 + -2 = -26
-26 + -6X + -3X + 3X2 + -1X2 = 2 + 3X + X2 + -2 + -3X + -1X2

Combine like terms: -6X + -3X = -9X
-26 + -9X + 3X2 + -1X2 = 2 + 3X + X2 + -2 + -3X + -1X2

Combine like terms: 3X2 + -1X2 = 2X2
-26 + -9X + 2X2 = 2 + 3X + X2 + -2 + -3X + -1X2

Reorder the terms:
-26 + -9X + 2X2 = 2 + -2 + 3X + -3X + X2 + -1X2

Combine like terms: 2 + -2 = 0
-26 + -9X + 2X2 = 0 + 3X + -3X + X2 + -1X2
-26 + -9X + 2X2 = 3X + -3X + X2 + -1X2

Combine like terms: 3X + -3X = 0
-26 + -9X + 2X2 = 0 + X2 + -1X2
-26 + -9X + 2X2 = X2 + -1X2

Combine like terms: X2 + -1X2 = 0
-26 + -9X + 2X2 = 0

Factor a trinomial.
(-2 + -1X)(13 + -2X) = 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 '(13 + -2X)' equal to zero and attempt to solve:

Simplifying
13 + -2X = 0

Solving
13 + -2X = 0

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

Add '-13' to each side of the equation.
13 + -13 + -2X = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2X = 0 + -13
-2X = 0 + -13

Combine like terms: 0 + -13 = -13
-2X = -13

Divide each side by '-2'.
X = 6.5

Simplifying
X = 6.5
Solution
X = {-2, 6.5}

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