(10r+7)(3r-9)=3

Solution for (10r+7)(3r-9)=3 equation:

Simplifying
(10r + 7)(3r + -9) = 3

Reorder the terms:
(7 + 10r)(3r + -9) = 3

Reorder the terms:
(7 + 10r)(-9 + 3r) = 3

Multiply (7 + 10r) * (-9 + 3r)
(7(-9 + 3r) + 10r * (-9 + 3r)) = 3
((-9 * 7 + 3r * 7) + 10r * (-9 + 3r)) = 3
((-63 + 21r) + 10r * (-9 + 3r)) = 3
(-63 + 21r + (-9 * 10r + 3r * 10r)) = 3
(-63 + 21r + (-90r + 30r2)) = 3

Combine like terms: 21r + -90r = -69r
(-63 + -69r + 30r2) = 3

Solving
-63 + -69r + 30r2 = 3

Solving for variable 'r'.

Reorder the terms:
-63 + -3 + -69r + 30r2 = 3 + -3

Combine like terms: -63 + -3 = -66
-66 + -69r + 30r2 = 3 + -3

Combine like terms: 3 + -3 = 0
-66 + -69r + 30r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-22 + -23r + 10r2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-22 + -23r + 10r2)' equal to zero and attempt to solve:

Simplifying
-22 + -23r + 10r2 = 0

Solving
-22 + -23r + 10r2 = 0

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

Divide each side by '10'.
-2.2 + -2.3r + r2 = 0.0

Move the constant term to the right:

Add '2.2' to each side of the equation.
-2.2 + -2.3r + 2.2 + r2 = 0.0 + 2.2

Reorder the terms:
-2.2 + 2.2 + -2.3r + r2 = 0.0 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + -2.3r + r2 = 0.0 + 2.2
-2.3r + r2 = 0.0 + 2.2

Combine like terms: 0.0 + 2.2 = 2.2
-2.3r + r2 = 2.2

The r term is -2.3r.  Take half its coefficient (-1.15).
Square it (1.3225) and add it to both sides.

Add '1.3225' to each side of the equation.
-2.3r + 1.3225 + r2 = 2.2 + 1.3225

Reorder the terms:
1.3225 + -2.3r + r2 = 2.2 + 1.3225

Combine like terms: 2.2 + 1.3225 = 3.5225
1.3225 + -2.3r + r2 = 3.5225

Factor a perfect square on the left side:
(r + -1.15)(r + -1.15) = 3.5225

Calculate the square root of the right side: 1.876832438

Break this problem into two subproblems by setting 
(r + -1.15) equal to 1.876832438 and -1.876832438.

Subproblem 1
r + -1.15 = 1.876832438

Simplifying
r + -1.15 = 1.876832438

Reorder the terms:
-1.15 + r = 1.876832438

Solving
-1.15 + r = 1.876832438

Solving for variable 'r'.

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

Add '1.15' to each side of the equation.
-1.15 + 1.15 + r = 1.876832438 + 1.15

Combine like terms: -1.15 + 1.15 = 0.00
0.00 + r = 1.876832438 + 1.15
r = 1.876832438 + 1.15

Combine like terms: 1.876832438 + 1.15 = 3.026832438
r = 3.026832438

Simplifying
r = 3.026832438

Subproblem 2
r + -1.15 = -1.876832438

Simplifying
r + -1.15 = -1.876832438

Reorder the terms:
-1.15 + r = -1.876832438

Solving
-1.15 + r = -1.876832438

Solving for variable 'r'.

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

Add '1.15' to each side of the equation.
-1.15 + 1.15 + r = -1.876832438 + 1.15

Combine like terms: -1.15 + 1.15 = 0.00
0.00 + r = -1.876832438 + 1.15
r = -1.876832438 + 1.15

Combine like terms: -1.876832438 + 1.15 = -0.726832438
r = -0.726832438

Simplifying
r = -0.726832438

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {3.026832438, -0.726832438}
Solution
r = {3.026832438, -0.726832438}