4r^2-8r-15=9

Solution for 4r^2-8r-15=9 equation:

Simplifying
4r2 + -8r + -15 = 9

Reorder the terms:
-15 + -8r + 4r2 = 9

Solving
-15 + -8r + 4r2 = 9

Solving for variable 'r'.

Reorder the terms:
-15 + -9 + -8r + 4r2 = 9 + -9

Combine like terms: -15 + -9 = -24
-24 + -8r + 4r2 = 9 + -9

Combine like terms: 9 + -9 = 0
-24 + -8r + 4r2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + -2r + r2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-6 + -2r + r2)' equal to zero and attempt to solve:

Simplifying
-6 + -2r + r2 = 0

Solving
-6 + -2r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -2r + 6 + r2 = 0 + 6

Reorder the terms:
-6 + 6 + -2r + r2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -2r + r2 = 0 + 6
-2r + r2 = 0 + 6

Combine like terms: 0 + 6 = 6
-2r + r2 = 6

The r term is -2r.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2r + 1 + r2 = 6 + 1

Reorder the terms:
1 + -2r + r2 = 6 + 1

Combine like terms: 6 + 1 = 7
1 + -2r + r2 = 7

Factor a perfect square on the left side:
(r + -1)(r + -1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(r + -1) equal to 2.645751311 and -2.645751311.

Subproblem 1
r + -1 = 2.645751311

Simplifying
r + -1 = 2.645751311

Reorder the terms:
-1 + r = 2.645751311

Solving
-1 + r = 2.645751311

Solving for variable 'r'.

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

Add '1' to each side of the equation.
-1 + 1 + r = 2.645751311 + 1

Combine like terms: -1 + 1 = 0
0 + r = 2.645751311 + 1
r = 2.645751311 + 1

Combine like terms: 2.645751311 + 1 = 3.645751311
r = 3.645751311

Simplifying
r = 3.645751311

Subproblem 2
r + -1 = -2.645751311

Simplifying
r + -1 = -2.645751311

Reorder the terms:
-1 + r = -2.645751311

Solving
-1 + r = -2.645751311

Solving for variable 'r'.

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

Add '1' to each side of the equation.
-1 + 1 + r = -2.645751311 + 1

Combine like terms: -1 + 1 = 0
0 + r = -2.645751311 + 1
r = -2.645751311 + 1

Combine like terms: -2.645751311 + 1 = -1.645751311
r = -1.645751311

Simplifying
r = -1.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {3.645751311, -1.645751311}
Solution
r = {3.645751311, -1.645751311}