-12r^2+28+42r=0

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Solution for -12r^2+28+42r=0 equation: 


Simplifying
-12r2 + 28 + 42r = 0

Reorder the terms:
28 + 42r + -12r2 = 0

Solving
28 + 42r + -12r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + 21r + -6r2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(14 + 21r + -6r2)' equal to zero and attempt to solve:

Simplifying
14 + 21r + -6r2 = 0

Solving
14 + 21r + -6r2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-2.333333333 + -3.5r + r2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -3.5r + 2.333333333 + r2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -3.5r + r2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -3.5r + r2 = 0 + 2.333333333
-3.5r + r2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-3.5r + r2 = 2.333333333

The r term is -3.5r.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5r + 3.0625 + r2 = 2.333333333 + 3.0625

Reorder the terms:
3.0625 + -3.5r + r2 = 2.333333333 + 3.0625

Combine like terms: 2.333333333 + 3.0625 = 5.395833333
3.0625 + -3.5r + r2 = 5.395833333

Factor a perfect square on the left side:
(r + -1.75)(r + -1.75) = 5.395833333

Calculate the square root of the right side: 2.322893311

Break this problem into two subproblems by setting 
(r + -1.75) equal to 2.322893311 and -2.322893311.


Subproblem 1
r + -1.75 = 2.322893311

Simplifying
r + -1.75 = 2.322893311

Reorder the terms:
-1.75 + r = 2.322893311

Solving
-1.75 + r = 2.322893311

Solving for variable 'r'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + r = 2.322893311 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + r = 2.322893311 + 1.75
r = 2.322893311 + 1.75

Combine like terms: 2.322893311 + 1.75 = 4.072893311
r = 4.072893311

Simplifying
r = 4.072893311


Subproblem 2
r + -1.75 = -2.322893311

Simplifying
r + -1.75 = -2.322893311

Reorder the terms:
-1.75 + r = -2.322893311

Solving
-1.75 + r = -2.322893311

Solving for variable 'r'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + r = -2.322893311 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + r = -2.322893311 + 1.75
r = -2.322893311 + 1.75

Combine like terms: -2.322893311 + 1.75 = -0.572893311
r = -0.572893311

Simplifying
r = -0.572893311


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {4.072893311, -0.572893311}
Solution
r = {4.072893311, -0.572893311}

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