-3(4r+9)+2(3r+8)=r(9r-5)

Solution for -3(4r+9)+2(3r+8)=r(9r-5) equation:

Simplifying
-3(4r + 9) + 2(3r + 8) = r(9r + -5)

Reorder the terms:
-3(9 + 4r) + 2(3r + 8) = r(9r + -5)
(9 * -3 + 4r * -3) + 2(3r + 8) = r(9r + -5)
(-27 + -12r) + 2(3r + 8) = r(9r + -5)

Reorder the terms:
-27 + -12r + 2(8 + 3r) = r(9r + -5)
-27 + -12r + (8 * 2 + 3r * 2) = r(9r + -5)
-27 + -12r + (16 + 6r) = r(9r + -5)

Reorder the terms:
-27 + 16 + -12r + 6r = r(9r + -5)

Combine like terms: -27 + 16 = -11
-11 + -12r + 6r = r(9r + -5)

Combine like terms: -12r + 6r = -6r
-11 + -6r = r(9r + -5)

Reorder the terms:
-11 + -6r = r(-5 + 9r)
-11 + -6r = (-5 * r + 9r * r)
-11 + -6r = (-5r + 9r2)

Solving
-11 + -6r = -5r + 9r2

Solving for variable 'r'.

Combine like terms: -6r + 5r = -1r
-11 + -1r + -9r2 = -5r + 9r2 + 5r + -9r2

Reorder the terms:
-11 + -1r + -9r2 = -5r + 5r + 9r2 + -9r2

Combine like terms: -5r + 5r = 0
-11 + -1r + -9r2 = 0 + 9r2 + -9r2
-11 + -1r + -9r2 = 9r2 + -9r2

Combine like terms: 9r2 + -9r2 = 0
-11 + -1r + -9r2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(11 + r + 9r2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(11 + r + 9r2)' equal to zero and attempt to solve:

Simplifying
11 + r + 9r2 = 0

Solving
11 + r + 9r2 = 0

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

Divide each side by '9'.
1.222222222 + 0.1111111111r + r2 = 0

Move the constant term to the right:

Add '-1.222222222' to each side of the equation.
1.222222222 + 0.1111111111r + -1.222222222 + r2 = 0 + -1.222222222

Reorder the terms:
1.222222222 + -1.222222222 + 0.1111111111r + r2 = 0 + -1.222222222

Combine like terms: 1.222222222 + -1.222222222 = 0.000000000
0.000000000 + 0.1111111111r + r2 = 0 + -1.222222222
0.1111111111r + r2 = 0 + -1.222222222

Combine like terms: 0 + -1.222222222 = -1.222222222
0.1111111111r + r2 = -1.222222222

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.
0.1111111111r + 0.25 + r2 = -1.222222222 + 0.25

Reorder the terms:
0.25 + 0.1111111111r + r2 = -1.222222222 + 0.25

Combine like terms: -1.222222222 + 0.25 = -0.972222222
0.25 + 0.1111111111r + r2 = -0.972222222

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = -0.972222222

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.