3r(r+4)+5(r+6)=

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Solution for 3r(r+4)+5(r+6)= equation: 


Simplifying
3r(r + 4) + 5(r + 6) = 0

Reorder the terms:
3r(4 + r) + 5(r + 6) = 0
(4 * 3r + r * 3r) + 5(r + 6) = 0
(12r + 3r2) + 5(r + 6) = 0

Reorder the terms:
12r + 3r2 + 5(6 + r) = 0
12r + 3r2 + (6 * 5 + r * 5) = 0
12r + 3r2 + (30 + 5r) = 0

Reorder the terms:
30 + 12r + 5r + 3r2 = 0

Combine like terms: 12r + 5r = 17r
30 + 17r + 3r2 = 0

Solving
30 + 17r + 3r2 = 0

Solving for variable 'r'.

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

Divide each side by '3'.
10 + 5.666666667r + r2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 5.666666667r + -10 + r2 = 0 + -10

Reorder the terms:
10 + -10 + 5.666666667r + r2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 5.666666667r + r2 = 0 + -10
5.666666667r + r2 = 0 + -10

Combine like terms: 0 + -10 = -10
5.666666667r + r2 = -10

The r term is 5.666666667r.  Take half its coefficient (2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
5.666666667r + 8.027777782 + r2 = -10 + 8.027777782

Reorder the terms:
8.027777782 + 5.666666667r + r2 = -10 + 8.027777782

Combine like terms: -10 + 8.027777782 = -1.972222218
8.027777782 + 5.666666667r + r2 = -1.972222218

Factor a perfect square on the left side:
(r + 2.833333334)(r + 2.833333334) = -1.972222218

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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