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 = 13
13 + 10r + -108r + -24r2 = 7 + 108r + 24r2 + -7 + -108r + -24r2

Combine like terms: 10r + -108r = -98r
13 + -98r + -24r2 = 7 + 108r + 24r2 + -7 + -108r + -24r2

Reorder the terms:
13 + -98r + -24r2 = 7 + -7 + 108r + -108r + 24r2 + -24r2

Combine like terms: 7 + -7 = 0
13 + -98r + -24r2 = 0 + 108r + -108r + 24r2 + -24r2
13 + -98r + -24r2 = 108r + -108r + 24r2 + -24r2

Combine like terms: 108r + -108r = 0
13 + -98r + -24r2 = 0 + 24r2 + -24r2
13 + -98r + -24r2 = 24r2 + -24r2

Combine like terms: 24r2 + -24r2 = 0
13 + -98r + -24r2 = 0

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

Divide each side by '-24'.
-0.5416666667 + 4.083333333r + r2 = 0

Move the constant term to the right:

Add '0.5416666667' to each side of the equation.
-0.5416666667 + 4.083333333r + 0.5416666667 + r2 = 0 + 0.5416666667

Reorder the terms:
-0.5416666667 + 0.5416666667 + 4.083333333r + r2 = 0 + 0.5416666667

Combine like terms: -0.5416666667 + 0.5416666667 = 0.0000000000
0.0000000000 + 4.083333333r + r2 = 0 + 0.5416666667
4.083333333r + r2 = 0 + 0.5416666667

Combine like terms: 0 + 0.5416666667 = 0.5416666667
4.083333333r + r2 = 0.5416666667

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 = 0.5416666667 + 4.168402779

Reorder the terms:
4.168402779 + 4.083333333r + r2 = 0.5416666667 + 4.168402779

Combine like terms: 0.5416666667 + 4.168402779 = 4.7100694457
4.168402779 + 4.083333333r + r2 = 4.7100694457

Factor a perfect square on the left side:
(r + 2.041666667)(r + 2.041666667) = 4.7100694457

Calculate the square root of the right side: 2.170269441

Break this problem into two subproblems by setting 
(r + 2.041666667) equal to 2.170269441 and -2.170269441.

Subproblem 1
r + 2.041666667 = 2.170269441

Simplifying
r + 2.041666667 = 2.170269441

Reorder the terms:
2.041666667 + r = 2.170269441

Solving
2.041666667 + r = 2.170269441

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 = 2.170269441 + -2.041666667

Combine like terms: 2.041666667 + -2.041666667 = 0.000000000
0.000000000 + r = 2.170269441 + -2.041666667
r = 2.170269441 + -2.041666667

Combine like terms: 2.170269441 + -2.041666667 = 0.128602774
r = 0.128602774

Simplifying
r = 0.128602774

Subproblem 2
r + 2.041666667 = -2.170269441

Simplifying
r + 2.041666667 = -2.170269441

Reorder the terms:
2.041666667 + r = -2.170269441

Solving
2.041666667 + r = -2.170269441

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 = -2.170269441 + -2.041666667

Combine like terms: 2.041666667 + -2.041666667 = 0.000000000
0.000000000 + r = -2.170269441 + -2.041666667
r = -2.170269441 + -2.041666667

Combine like terms: -2.170269441 + -2.041666667 = -4.211936108
r = -4.211936108

Simplifying
r = -4.211936108

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.128602774, -4.211936108}