288-115r=8-10r^2

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Solution for 288-115r=8-10r^2 equation: 


Simplifying
288 + -115r = 8 + -10r2

Solving
288 + -115r = 8 + -10r2

Solving for variable 'r'.

Reorder the terms:
288 + -8 + -115r + 10r2 = 8 + -10r2 + -8 + 10r2

Combine like terms: 288 + -8 = 280
280 + -115r + 10r2 = 8 + -10r2 + -8 + 10r2

Reorder the terms:
280 + -115r + 10r2 = 8 + -8 + -10r2 + 10r2

Combine like terms: 8 + -8 = 0
280 + -115r + 10r2 = 0 + -10r2 + 10r2
280 + -115r + 10r2 = -10r2 + 10r2

Combine like terms: -10r2 + 10r2 = 0
280 + -115r + 10r2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(56 + -23r + 2r2) = 0

Factor a trinomial.
5((7 + -2r)(8 + -1r)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(7 + -2r)' equal to zero and attempt to solve:

Simplifying
7 + -2r = 0

Solving
7 + -2r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2r = 0 + -7
-2r = 0 + -7

Combine like terms: 0 + -7 = -7
-2r = -7

Divide each side by '-2'.
r = 3.5

Simplifying
r = 3.5

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 = {3.5, 8}

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