r^2-r-2=(2r-1)(r-3)

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Solution for r^2-r-2=(2r-1)(r-3) equation: 


Simplifying
r2 + -1r + -2 = (2r + -1)(r + -3)

Reorder the terms:
-2 + -1r + r2 = (2r + -1)(r + -3)

Reorder the terms:
-2 + -1r + r2 = (-1 + 2r)(r + -3)

Reorder the terms:
-2 + -1r + r2 = (-1 + 2r)(-3 + r)

Multiply (-1 + 2r) * (-3 + r)
-2 + -1r + r2 = (-1(-3 + r) + 2r * (-3 + r))
-2 + -1r + r2 = ((-3 * -1 + r * -1) + 2r * (-3 + r))
-2 + -1r + r2 = ((3 + -1r) + 2r * (-3 + r))
-2 + -1r + r2 = (3 + -1r + (-3 * 2r + r * 2r))
-2 + -1r + r2 = (3 + -1r + (-6r + 2r2))

Combine like terms: -1r + -6r = -7r
-2 + -1r + r2 = (3 + -7r + 2r2)

Solving
-2 + -1r + r2 = 3 + -7r + 2r2

Solving for variable 'r'.

Reorder the terms:
-2 + -3 + -1r + 7r + r2 + -2r2 = 3 + -7r + 2r2 + -3 + 7r + -2r2

Combine like terms: -2 + -3 = -5
-5 + -1r + 7r + r2 + -2r2 = 3 + -7r + 2r2 + -3 + 7r + -2r2

Combine like terms: -1r + 7r = 6r
-5 + 6r + r2 + -2r2 = 3 + -7r + 2r2 + -3 + 7r + -2r2

Combine like terms: r2 + -2r2 = -1r2
-5 + 6r + -1r2 = 3 + -7r + 2r2 + -3 + 7r + -2r2

Reorder the terms:
-5 + 6r + -1r2 = 3 + -3 + -7r + 7r + 2r2 + -2r2

Combine like terms: 3 + -3 = 0
-5 + 6r + -1r2 = 0 + -7r + 7r + 2r2 + -2r2
-5 + 6r + -1r2 = -7r + 7r + 2r2 + -2r2

Combine like terms: -7r + 7r = 0
-5 + 6r + -1r2 = 0 + 2r2 + -2r2
-5 + 6r + -1r2 = 2r2 + -2r2

Combine like terms: 2r2 + -2r2 = 0
-5 + 6r + -1r2 = 0

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


Subproblem 1
Set the factor '(-5 + r)' equal to zero and attempt to solve:

Simplifying
-5 + r = 0

Solving
-5 + r = 0

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

Add '5' to each side of the equation.
-5 + 5 + r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + r = 0 + 5
r = 0 + 5

Combine like terms: 0 + 5 = 5
r = 5

Simplifying
r = 5

Subproblem 2
Set the factor '(1 + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1r = 0

Solving
1 + -1r = 0

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

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

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

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

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

Simplifying
r = 1
Solution
r = {5, 1}

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