2r(11+2r)+6r(-2r+4)=

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Solution for 2r(11+2r)+6r(-2r+4)= equation: 


Simplifying
2r(11 + 2r) + 6r(-2r + 4) = 0
(11 * 2r + 2r * 2r) + 6r(-2r + 4) = 0
(22r + 4r2) + 6r(-2r + 4) = 0

Reorder the terms:
22r + 4r2 + 6r(4 + -2r) = 0
22r + 4r2 + (4 * 6r + -2r * 6r) = 0
22r + 4r2 + (24r + -12r2) = 0

Reorder the terms:
22r + 24r + 4r2 + -12r2 = 0

Combine like terms: 22r + 24r = 46r
46r + 4r2 + -12r2 = 0

Combine like terms: 4r2 + -12r2 = -8r2
46r + -8r2 = 0

Solving
46r + -8r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2r'.
2r(23 + -4r) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0

Subproblem 2
Set the factor '(23 + -4r)' equal to zero and attempt to solve:

Simplifying
23 + -4r = 0

Solving
23 + -4r = 0

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

Add '-23' to each side of the equation.
23 + -23 + -4r = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -4r = 0 + -23
-4r = 0 + -23

Combine like terms: 0 + -23 = -23
-4r = -23

Divide each side by '-4'.
r = 5.75

Simplifying
r = 5.75
Solution
r = {0, 5.75}

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