5(2r+4)=3(2r+9)4r-7

Solution for 5(2r+4)=3(2r+9)4r-7 equation:

Simplifying
5(2r + 4) = 3(2r + 9) * 4r + -7

Reorder the terms:
5(4 + 2r) = 3(2r + 9) * 4r + -7
(4 * 5 + 2r * 5) = 3(2r + 9) * 4r + -7
(20 + 10r) = 3(2r + 9) * 4r + -7

Reorder the terms:
20 + 10r = 3(9 + 2r) * 4r + -7

Reorder the terms for easier multiplication:
20 + 10r = 3 * 4r(9 + 2r) + -7

Multiply 3 * 4
20 + 10r = 12r(9 + 2r) + -7
20 + 10r = (9 * 12r + 2r * 12r) + -7
20 + 10r = (108r + 24r2) + -7

Reorder the terms:
20 + 10r = -7 + 108r + 24r2

Solving
20 + 10r = -7 + 108r + 24r2

Solving for variable 'r'.

Reorder the terms:
20 + 7 + 10r + -108r + -24r2 = -7 + 108r + 24r2 + 7 + -108r + -24r2

Combine like terms: 20 + 7 = 27
27 + 10r + -108r + -24r2 = -7 + 108r + 24r2 + 7 + -108r + -24r2

Combine like terms: 10r + -108r = -98r
27 + -98r + -24r2 = -7 + 108r + 24r2 + 7 + -108r + -24r2

Reorder the terms:
27 + -98r + -24r2 = -7 + 7 + 108r + -108r + 24r2 + -24r2

Combine like terms: -7 + 7 = 0
27 + -98r + -24r2 = 0 + 108r + -108r + 24r2 + -24r2
27 + -98r + -24r2 = 108r + -108r + 24r2 + -24r2

Combine like terms: 108r + -108r = 0
27 + -98r + -24r2 = 0 + 24r2 + -24r2
27 + -98r + -24r2 = 24r2 + -24r2

Combine like terms: 24r2 + -24r2 = 0
27 + -98r + -24r2 = 0

Begin completing the square.  Divide all terms by
-24 the coefficient of the squared term: 

Divide each side by '-24'.
-1.125 + 4.083333333r + r2 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + 4.083333333r + 1.125 + r2 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + 4.083333333r + r2 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + 4.083333333r + r2 = 0 + 1.125
4.083333333r + r2 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
4.083333333r + r2 = 1.125

The r term is 4.083333333r.  Take half its coefficient (2.041666667).
Square it (4.168402779) and add it to both sides.

Add '4.168402779' to each side of the equation.
4.083333333r + 4.168402779 + r2 = 1.125 + 4.168402779

Reorder the terms:
4.168402779 + 4.083333333r + r2 = 1.125 + 4.168402779

Combine like terms: 1.125 + 4.168402779 = 5.293402779
4.168402779 + 4.083333333r + r2 = 5.293402779

Factor a perfect square on the left side:
(r + 2.041666667)(r + 2.041666667) = 5.293402779

Calculate the square root of the right side: 2.300739616

Break this problem into two subproblems by setting 
(r + 2.041666667) equal to 2.300739616 and -2.300739616.

Subproblem 1
r + 2.041666667 = 2.300739616

Simplifying
r + 2.041666667 = 2.300739616

Reorder the terms:
2.041666667 + r = 2.300739616

Solving
2.041666667 + r = 2.300739616

Solving for variable 'r'.

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

Add '-2.041666667' to each side of the equation.
2.041666667 + -2.041666667 + r = 2.300739616 + -2.041666667

Combine like terms: 2.041666667 + -2.041666667 = 0.000000000
0.000000000 + r = 2.300739616 + -2.041666667
r = 2.300739616 + -2.041666667

Combine like terms: 2.300739616 + -2.041666667 = 0.259072949
r = 0.259072949

Simplifying
r = 0.259072949

Subproblem 2
r + 2.041666667 = -2.300739616

Simplifying
r + 2.041666667 = -2.300739616

Reorder the terms:
2.041666667 + r = -2.300739616

Solving
2.041666667 + r = -2.300739616

Solving for variable 'r'.

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

Add '-2.041666667' to each side of the equation.
2.041666667 + -2.041666667 + r = -2.300739616 + -2.041666667

Combine like terms: 2.041666667 + -2.041666667 = 0.000000000
0.000000000 + r = -2.300739616 + -2.041666667
r = -2.300739616 + -2.041666667

Combine like terms: -2.300739616 + -2.041666667 = -4.342406283
r = -4.342406283

Simplifying
r = -4.342406283

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.259072949, -4.342406283}