5r^2+2r+52=4r^2+12r+27

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Solution for 5r^2+2r+52=4r^2+12r+27 equation: 


Simplifying
5r2 + 2r + 52 = 4r2 + 12r + 27

Reorder the terms:
52 + 2r + 5r2 = 4r2 + 12r + 27

Reorder the terms:
52 + 2r + 5r2 = 27 + 12r + 4r2

Solving
52 + 2r + 5r2 = 27 + 12r + 4r2

Solving for variable 'r'.

Reorder the terms:
52 + -27 + 2r + -12r + 5r2 + -4r2 = 27 + 12r + 4r2 + -27 + -12r + -4r2

Combine like terms: 52 + -27 = 25
25 + 2r + -12r + 5r2 + -4r2 = 27 + 12r + 4r2 + -27 + -12r + -4r2

Combine like terms: 2r + -12r = -10r
25 + -10r + 5r2 + -4r2 = 27 + 12r + 4r2 + -27 + -12r + -4r2

Combine like terms: 5r2 + -4r2 = 1r2
25 + -10r + 1r2 = 27 + 12r + 4r2 + -27 + -12r + -4r2

Reorder the terms:
25 + -10r + 1r2 = 27 + -27 + 12r + -12r + 4r2 + -4r2

Combine like terms: 27 + -27 = 0
25 + -10r + 1r2 = 0 + 12r + -12r + 4r2 + -4r2
25 + -10r + 1r2 = 12r + -12r + 4r2 + -4r2

Combine like terms: 12r + -12r = 0
25 + -10r + 1r2 = 0 + 4r2 + -4r2
25 + -10r + 1r2 = 4r2 + -4r2

Combine like terms: 4r2 + -4r2 = 0
25 + -10r + 1r2 = 0

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


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

Simplifying
5 + -1r = 0

Solving
5 + -1r = 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 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5

Subproblem 2
Set the factor '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 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 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

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

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