(3X-8)(X+1)=(X+1)(X-3)

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Solution for (3X-8)(X+1)=(X+1)(X-3) equation: 


Simplifying
(3X + -8)(X + 1) = (X + 1)(X + -3)

Reorder the terms:
(-8 + 3X)(X + 1) = (X + 1)(X + -3)

Reorder the terms:
(-8 + 3X)(1 + X) = (X + 1)(X + -3)

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

Combine like terms: -8X + 3X = -5X
(-8 + -5X + 3X2) = (X + 1)(X + -3)

Reorder the terms:
-8 + -5X + 3X2 = (1 + X)(X + -3)

Reorder the terms:
-8 + -5X + 3X2 = (1 + X)(-3 + X)

Multiply (1 + X) * (-3 + X)
-8 + -5X + 3X2 = (1(-3 + X) + X(-3 + X))
-8 + -5X + 3X2 = ((-3 * 1 + X * 1) + X(-3 + X))
-8 + -5X + 3X2 = ((-3 + 1X) + X(-3 + X))
-8 + -5X + 3X2 = (-3 + 1X + (-3 * X + X * X))
-8 + -5X + 3X2 = (-3 + 1X + (-3X + X2))

Combine like terms: 1X + -3X = -2X
-8 + -5X + 3X2 = (-3 + -2X + X2)

Solving
-8 + -5X + 3X2 = -3 + -2X + X2

Solving for variable 'X'.

Reorder the terms:
-8 + 3 + -5X + 2X + 3X2 + -1X2 = -3 + -2X + X2 + 3 + 2X + -1X2

Combine like terms: -8 + 3 = -5
-5 + -5X + 2X + 3X2 + -1X2 = -3 + -2X + X2 + 3 + 2X + -1X2

Combine like terms: -5X + 2X = -3X
-5 + -3X + 3X2 + -1X2 = -3 + -2X + X2 + 3 + 2X + -1X2

Combine like terms: 3X2 + -1X2 = 2X2
-5 + -3X + 2X2 = -3 + -2X + X2 + 3 + 2X + -1X2

Reorder the terms:
-5 + -3X + 2X2 = -3 + 3 + -2X + 2X + X2 + -1X2

Combine like terms: -3 + 3 = 0
-5 + -3X + 2X2 = 0 + -2X + 2X + X2 + -1X2
-5 + -3X + 2X2 = -2X + 2X + X2 + -1X2

Combine like terms: -2X + 2X = 0
-5 + -3X + 2X2 = 0 + X2 + -1X2
-5 + -3X + 2X2 = X2 + -1X2

Combine like terms: X2 + -1X2 = 0
-5 + -3X + 2X2 = 0

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


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

Simplifying
-1 + -1X = 0

Solving
-1 + -1X = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1X = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1X = 0 + 1
-1X = 0 + 1

Combine like terms: 0 + 1 = 1
-1X = 1

Divide each side by '-1'.
X = -1

Simplifying
X = -1

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

Simplifying
5 + -2X = 0

Solving
5 + -2X = 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 + -2X = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2X = 0 + -5
-2X = 0 + -5

Combine like terms: 0 + -5 = -5
-2X = -5

Divide each side by '-2'.
X = 2.5

Simplifying
X = 2.5
Solution
X = {-1, 2.5}

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