25r^2-15=4r^2-r+35

Solution for 25r^2-15=4r^2-r+35 equation:

Simplifying
25r2 + -15 = 4r2 + -1r + 35

Reorder the terms:
-15 + 25r2 = 4r2 + -1r + 35

Reorder the terms:
-15 + 25r2 = 35 + -1r + 4r2

Solving
-15 + 25r2 = 35 + -1r + 4r2

Solving for variable 'r'.

Reorder the terms:
-15 + -35 + r + 25r2 + -4r2 = 35 + -1r + 4r2 + -35 + r + -4r2

Combine like terms: -15 + -35 = -50
-50 + r + 25r2 + -4r2 = 35 + -1r + 4r2 + -35 + r + -4r2

Combine like terms: 25r2 + -4r2 = 21r2
-50 + r + 21r2 = 35 + -1r + 4r2 + -35 + r + -4r2

Reorder the terms:
-50 + r + 21r2 = 35 + -35 + -1r + r + 4r2 + -4r2

Combine like terms: 35 + -35 = 0
-50 + r + 21r2 = 0 + -1r + r + 4r2 + -4r2
-50 + r + 21r2 = -1r + r + 4r2 + -4r2

Combine like terms: -1r + r = 0
-50 + r + 21r2 = 0 + 4r2 + -4r2
-50 + r + 21r2 = 4r2 + -4r2

Combine like terms: 4r2 + -4r2 = 0
-50 + r + 21r2 = 0

Begin completing the square.  Divide all terms by
21 the coefficient of the squared term: 

Divide each side by '21'.
-2.380952381 + 0.04761904762r + r2 = 0

Move the constant term to the right:

Add '2.380952381' to each side of the equation.
-2.380952381 + 0.04761904762r + 2.380952381 + r2 = 0 + 2.380952381

Reorder the terms:
-2.380952381 + 2.380952381 + 0.04761904762r + r2 = 0 + 2.380952381

Combine like terms: -2.380952381 + 2.380952381 = 0.000000000
0.000000000 + 0.04761904762r + r2 = 0 + 2.380952381
0.04761904762r + r2 = 0 + 2.380952381

Combine like terms: 0 + 2.380952381 = 2.380952381
0.04761904762r + r2 = 2.380952381

The r term is r.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.04761904762r + 0.25 + r2 = 2.380952381 + 0.25

Reorder the terms:
0.25 + 0.04761904762r + r2 = 2.380952381 + 0.25

Combine like terms: 2.380952381 + 0.25 = 2.630952381
0.25 + 0.04761904762r + r2 = 2.630952381

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = 2.630952381

Calculate the square root of the right side: 1.622021079

Break this problem into two subproblems by setting 
(r + 0.5) equal to 1.622021079 and -1.622021079.

Subproblem 1
r + 0.5 = 1.622021079

Simplifying
r + 0.5 = 1.622021079

Reorder the terms:
0.5 + r = 1.622021079

Solving
0.5 + r = 1.622021079

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = 1.622021079 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = 1.622021079 + -0.5
r = 1.622021079 + -0.5

Combine like terms: 1.622021079 + -0.5 = 1.122021079
r = 1.122021079

Simplifying
r = 1.122021079

Subproblem 2
r + 0.5 = -1.622021079

Simplifying
r + 0.5 = -1.622021079

Reorder the terms:
0.5 + r = -1.622021079

Solving
0.5 + r = -1.622021079

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = -1.622021079 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = -1.622021079 + -0.5
r = -1.622021079 + -0.5

Combine like terms: -1.622021079 + -0.5 = -2.122021079
r = -2.122021079

Simplifying
r = -2.122021079

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {1.122021079, -2.122021079}