4(3r^2-50r-28)=0

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Solution for 4(3r^2-50r-28)=0 equation: 


Simplifying
4(3r2 + -50r + -28) = 0

Reorder the terms:
4(-28 + -50r + 3r2) = 0
(-28 * 4 + -50r * 4 + 3r2 * 4) = 0
(-112 + -200r + 12r2) = 0

Solving
-112 + -200r + 12r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-28 + -50r + 3r2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-28 + -50r + 3r2)' equal to zero and attempt to solve:

Simplifying
-28 + -50r + 3r2 = 0

Solving
-28 + -50r + 3r2 = 0

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

Divide each side by '3'.
-9.333333333 + -16.66666667r + r2 = 0

Move the constant term to the right:

Add '9.333333333' to each side of the equation.
-9.333333333 + -16.66666667r + 9.333333333 + r2 = 0 + 9.333333333

Reorder the terms:
-9.333333333 + 9.333333333 + -16.66666667r + r2 = 0 + 9.333333333

Combine like terms: -9.333333333 + 9.333333333 = 0.000000000
0.000000000 + -16.66666667r + r2 = 0 + 9.333333333
-16.66666667r + r2 = 0 + 9.333333333

Combine like terms: 0 + 9.333333333 = 9.333333333
-16.66666667r + r2 = 9.333333333

The r term is -16.66666667r.  Take half its coefficient (-8.333333335).
Square it (69.44444447) and add it to both sides.

Add '69.44444447' to each side of the equation.
-16.66666667r + 69.44444447 + r2 = 9.333333333 + 69.44444447

Reorder the terms:
69.44444447 + -16.66666667r + r2 = 9.333333333 + 69.44444447

Combine like terms: 9.333333333 + 69.44444447 = 78.777777803
69.44444447 + -16.66666667r + r2 = 78.777777803

Factor a perfect square on the left side:
(r + -8.333333335)(r + -8.333333335) = 78.777777803

Calculate the square root of the right side: 8.875684639

Break this problem into two subproblems by setting 
(r + -8.333333335) equal to 8.875684639 and -8.875684639.


Subproblem 1
r + -8.333333335 = 8.875684639

Simplifying
r + -8.333333335 = 8.875684639

Reorder the terms:
-8.333333335 + r = 8.875684639

Solving
-8.333333335 + r = 8.875684639

Solving for variable 'r'.

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

Add '8.333333335' to each side of the equation.
-8.333333335 + 8.333333335 + r = 8.875684639 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + r = 8.875684639 + 8.333333335
r = 8.875684639 + 8.333333335

Combine like terms: 8.875684639 + 8.333333335 = 17.209017974
r = 17.209017974

Simplifying
r = 17.209017974


Subproblem 2
r + -8.333333335 = -8.875684639

Simplifying
r + -8.333333335 = -8.875684639

Reorder the terms:
-8.333333335 + r = -8.875684639

Solving
-8.333333335 + r = -8.875684639

Solving for variable 'r'.

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

Add '8.333333335' to each side of the equation.
-8.333333335 + 8.333333335 + r = -8.875684639 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + r = -8.875684639 + 8.333333335
r = -8.875684639 + 8.333333335

Combine like terms: -8.875684639 + 8.333333335 = -0.542351304
r = -0.542351304

Simplifying
r = -0.542351304


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {17.209017974, -0.542351304}
Solution
r = {17.209017974, -0.542351304}

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