12r^2-42r+972=0

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Solution for 12r^2-42r+972=0 equation: 


Simplifying
12r2 + -42r + 972 = 0

Reorder the terms:
972 + -42r + 12r2 = 0

Solving
972 + -42r + 12r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '6'.
6(162 + -7r + 2r2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(162 + -7r + 2r2)' equal to zero and attempt to solve:

Simplifying
162 + -7r + 2r2 = 0

Solving
162 + -7r + 2r2 = 0

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

Divide each side by '2'.
81 + -3.5r + r2 = 0

Move the constant term to the right:

Add '-81' to each side of the equation.
81 + -3.5r + -81 + r2 = 0 + -81

Reorder the terms:
81 + -81 + -3.5r + r2 = 0 + -81

Combine like terms: 81 + -81 = 0
0 + -3.5r + r2 = 0 + -81
-3.5r + r2 = 0 + -81

Combine like terms: 0 + -81 = -81
-3.5r + r2 = -81

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 = -81 + 3.0625

Reorder the terms:
3.0625 + -3.5r + r2 = -81 + 3.0625

Combine like terms: -81 + 3.0625 = -77.9375
3.0625 + -3.5r + r2 = -77.9375

Factor a perfect square on the left side:
(r + -1.75)(r + -1.75) = -77.9375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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