6r^2-42r+60=r^2-6r+8

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Solution for 6r^2-42r+60=r^2-6r+8 equation: 


Simplifying
6r2 + -42r + 60 = r2 + -6r + 8

Reorder the terms:
60 + -42r + 6r2 = r2 + -6r + 8

Reorder the terms:
60 + -42r + 6r2 = 8 + -6r + r2

Solving
60 + -42r + 6r2 = 8 + -6r + r2

Solving for variable 'r'.

Reorder the terms:
60 + -8 + -42r + 6r + 6r2 + -1r2 = 8 + -6r + r2 + -8 + 6r + -1r2

Combine like terms: 60 + -8 = 52
52 + -42r + 6r + 6r2 + -1r2 = 8 + -6r + r2 + -8 + 6r + -1r2

Combine like terms: -42r + 6r = -36r
52 + -36r + 6r2 + -1r2 = 8 + -6r + r2 + -8 + 6r + -1r2

Combine like terms: 6r2 + -1r2 = 5r2
52 + -36r + 5r2 = 8 + -6r + r2 + -8 + 6r + -1r2

Reorder the terms:
52 + -36r + 5r2 = 8 + -8 + -6r + 6r + r2 + -1r2

Combine like terms: 8 + -8 = 0
52 + -36r + 5r2 = 0 + -6r + 6r + r2 + -1r2
52 + -36r + 5r2 = -6r + 6r + r2 + -1r2

Combine like terms: -6r + 6r = 0
52 + -36r + 5r2 = 0 + r2 + -1r2
52 + -36r + 5r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
52 + -36r + 5r2 = 0

Factor a trinomial.
(2 + -1r)(26 + -5r) = 0


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

Simplifying
2 + -1r = 0

Solving
2 + -1r = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1r = 0 + -2
-1r = 0 + -2

Combine like terms: 0 + -2 = -2
-1r = -2

Divide each side by '-1'.
r = 2

Simplifying
r = 2

Subproblem 2
Set the factor '(26 + -5r)' equal to zero and attempt to solve:

Simplifying
26 + -5r = 0

Solving
26 + -5r = 0

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

Add '-26' to each side of the equation.
26 + -26 + -5r = 0 + -26

Combine like terms: 26 + -26 = 0
0 + -5r = 0 + -26
-5r = 0 + -26

Combine like terms: 0 + -26 = -26
-5r = -26

Divide each side by '-5'.
r = 5.2

Simplifying
r = 5.2
Solution
r = {2, 5.2}

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