16r^2-6+24r-9=

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Solution for 16r^2-6+24r-9= equation: 


Simplifying
16r2 + -6 + 24r + -9 = 0

Reorder the terms:
-6 + -9 + 24r + 16r2 = 0

Combine like terms: -6 + -9 = -15
-15 + 24r + 16r2 = 0

Solving
-15 + 24r + 16r2 = 0

Solving for variable 'r'.

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

Divide each side by '16'.
-0.9375 + 1.5r + r2 = 0

Move the constant term to the right:

Add '0.9375' to each side of the equation.
-0.9375 + 1.5r + 0.9375 + r2 = 0 + 0.9375

Reorder the terms:
-0.9375 + 0.9375 + 1.5r + r2 = 0 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + 1.5r + r2 = 0 + 0.9375
1.5r + r2 = 0 + 0.9375

Combine like terms: 0 + 0.9375 = 0.9375
1.5r + r2 = 0.9375

The r term is 1.5r.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5r + 0.5625 + r2 = 0.9375 + 0.5625

Reorder the terms:
0.5625 + 1.5r + r2 = 0.9375 + 0.5625

Combine like terms: 0.9375 + 0.5625 = 1.5
0.5625 + 1.5r + r2 = 1.5

Factor a perfect square on the left side:
(r + 0.75)(r + 0.75) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(r + 0.75) equal to 1.224744871 and -1.224744871.


Subproblem 1
r + 0.75 = 1.224744871

Simplifying
r + 0.75 = 1.224744871

Reorder the terms:
0.75 + r = 1.224744871

Solving
0.75 + r = 1.224744871

Solving for variable 'r'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + r = 1.224744871 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + r = 1.224744871 + -0.75
r = 1.224744871 + -0.75

Combine like terms: 1.224744871 + -0.75 = 0.474744871
r = 0.474744871

Simplifying
r = 0.474744871


Subproblem 2
r + 0.75 = -1.224744871

Simplifying
r + 0.75 = -1.224744871

Reorder the terms:
0.75 + r = -1.224744871

Solving
0.75 + r = -1.224744871

Solving for variable 'r'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + r = -1.224744871 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + r = -1.224744871 + -0.75
r = -1.224744871 + -0.75

Combine like terms: -1.224744871 + -0.75 = -1.974744871
r = -1.974744871

Simplifying
r = -1.974744871


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.474744871, -1.974744871}

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