6(2r-11)-3r(r-2)=

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Solution for 6(2r-11)-3r(r-2)= equation: 


Simplifying
6(2r + -11) + -3r(r + -2) = 0

Reorder the terms:
6(-11 + 2r) + -3r(r + -2) = 0
(-11 * 6 + 2r * 6) + -3r(r + -2) = 0
(-66 + 12r) + -3r(r + -2) = 0

Reorder the terms:
-66 + 12r + -3r(-2 + r) = 0
-66 + 12r + (-2 * -3r + r * -3r) = 0
-66 + 12r + (6r + -3r2) = 0

Combine like terms: 12r + 6r = 18r
-66 + 18r + -3r2 = 0

Solving
-66 + 18r + -3r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-22 + 6r + -1r2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-22 + 6r + -1r2)' equal to zero and attempt to solve:

Simplifying
-22 + 6r + -1r2 = 0

Solving
-22 + 6r + -1r2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
22 + -6r + r2 = 0

Move the constant term to the right:

Add '-22' to each side of the equation.
22 + -6r + -22 + r2 = 0 + -22

Reorder the terms:
22 + -22 + -6r + r2 = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -6r + r2 = 0 + -22
-6r + r2 = 0 + -22

Combine like terms: 0 + -22 = -22
-6r + r2 = -22

The r term is -6r.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6r + 9 + r2 = -22 + 9

Reorder the terms:
9 + -6r + r2 = -22 + 9

Combine like terms: -22 + 9 = -13
9 + -6r + r2 = -13

Factor a perfect square on the left side:
(r + -3)(r + -3) = -13

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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