11r^2+3=25r+8r^2-5

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Solution for 11r^2+3=25r+8r^2-5 equation: 


Simplifying
11r2 + 3 = 25r + 8r2 + -5

Reorder the terms:
3 + 11r2 = 25r + 8r2 + -5

Reorder the terms:
3 + 11r2 = -5 + 25r + 8r2

Solving
3 + 11r2 = -5 + 25r + 8r2

Solving for variable 'r'.

Reorder the terms:
3 + 5 + -25r + 11r2 + -8r2 = -5 + 25r + 8r2 + 5 + -25r + -8r2

Combine like terms: 3 + 5 = 8
8 + -25r + 11r2 + -8r2 = -5 + 25r + 8r2 + 5 + -25r + -8r2

Combine like terms: 11r2 + -8r2 = 3r2
8 + -25r + 3r2 = -5 + 25r + 8r2 + 5 + -25r + -8r2

Reorder the terms:
8 + -25r + 3r2 = -5 + 5 + 25r + -25r + 8r2 + -8r2

Combine like terms: -5 + 5 = 0
8 + -25r + 3r2 = 0 + 25r + -25r + 8r2 + -8r2
8 + -25r + 3r2 = 25r + -25r + 8r2 + -8r2

Combine like terms: 25r + -25r = 0
8 + -25r + 3r2 = 0 + 8r2 + -8r2
8 + -25r + 3r2 = 8r2 + -8r2

Combine like terms: 8r2 + -8r2 = 0
8 + -25r + 3r2 = 0

Factor a trinomial.
(1 + -3r)(8 + -1r) = 0


Subproblem 1
Set the factor '(1 + -3r)' equal to zero and attempt to solve:

Simplifying
1 + -3r = 0

Solving
1 + -3r = 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 + -3r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3r = 0 + -1
-3r = 0 + -1

Combine like terms: 0 + -1 = -1
-3r = -1

Divide each side by '-3'.
r = 0.3333333333

Simplifying
r = 0.3333333333

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 = {0.3333333333, 8}

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