3r^2+r-16=2r^2-8+8r

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Solution for 3r^2+r-16=2r^2-8+8r equation: 


Simplifying
3r2 + r + -16 = 2r2 + -8 + 8r

Reorder the terms:
-16 + r + 3r2 = 2r2 + -8 + 8r

Reorder the terms:
-16 + r + 3r2 = -8 + 8r + 2r2

Solving
-16 + r + 3r2 = -8 + 8r + 2r2

Solving for variable 'r'.

Reorder the terms:
-16 + 8 + r + -8r + 3r2 + -2r2 = -8 + 8r + 2r2 + 8 + -8r + -2r2

Combine like terms: -16 + 8 = -8
-8 + r + -8r + 3r2 + -2r2 = -8 + 8r + 2r2 + 8 + -8r + -2r2

Combine like terms: r + -8r = -7r
-8 + -7r + 3r2 + -2r2 = -8 + 8r + 2r2 + 8 + -8r + -2r2

Combine like terms: 3r2 + -2r2 = 1r2
-8 + -7r + 1r2 = -8 + 8r + 2r2 + 8 + -8r + -2r2

Reorder the terms:
-8 + -7r + 1r2 = -8 + 8 + 8r + -8r + 2r2 + -2r2

Combine like terms: -8 + 8 = 0
-8 + -7r + 1r2 = 0 + 8r + -8r + 2r2 + -2r2
-8 + -7r + 1r2 = 8r + -8r + 2r2 + -2r2

Combine like terms: 8r + -8r = 0
-8 + -7r + 1r2 = 0 + 2r2 + -2r2
-8 + -7r + 1r2 = 2r2 + -2r2

Combine like terms: 2r2 + -2r2 = 0
-8 + -7r + 1r2 = 0

Factor a trinomial.
(-1 + -1r)(8 + -1r) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(8 + -1r)' equal to zero and attempt to solve:

Simplifying
8 + -1r = 0

Solving
8 + -1r = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1r = 0 + -8
-1r = 0 + -8

Combine like terms: 0 + -8 = -8
-1r = -8

Divide each side by '-1'.
r = 8

Simplifying
r = 8
Solution
r = {-1, 8}

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