4r(2r^2-3r+5)+6r(4r^2+2r+8)=0

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Solution for 4r(2r^2-3r+5)+6r(4r^2+2r+8)=0 equation: 


Simplifying
4r(2r2 + -3r + 5) + 6r(4r2 + 2r + 8) = 0

Reorder the terms:
4r(5 + -3r + 2r2) + 6r(4r2 + 2r + 8) = 0
(5 * 4r + -3r * 4r + 2r2 * 4r) + 6r(4r2 + 2r + 8) = 0
(20r + -12r2 + 8r3) + 6r(4r2 + 2r + 8) = 0

Reorder the terms:
20r + -12r2 + 8r3 + 6r(8 + 2r + 4r2) = 0
20r + -12r2 + 8r3 + (8 * 6r + 2r * 6r + 4r2 * 6r) = 0
20r + -12r2 + 8r3 + (48r + 12r2 + 24r3) = 0

Reorder the terms:
20r + 48r + -12r2 + 12r2 + 8r3 + 24r3 = 0

Combine like terms: 20r + 48r = 68r
68r + -12r2 + 12r2 + 8r3 + 24r3 = 0

Combine like terms: -12r2 + 12r2 = 0
68r + 0 + 8r3 + 24r3 = 0
68r + 8r3 + 24r3 = 0

Combine like terms: 8r3 + 24r3 = 32r3
68r + 32r3 = 0

Solving
68r + 32r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4r'.
4r(17 + 8r2) = 0

Ignore the factor 4.

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 '(17 + 8r2)' equal to zero and attempt to solve:

Simplifying
17 + 8r2 = 0

Solving
17 + 8r2 = 0

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

Add '-17' to each side of the equation.
17 + -17 + 8r2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + 8r2 = 0 + -17
8r2 = 0 + -17

Combine like terms: 0 + -17 = -17
8r2 = -17

Divide each side by '8'.
r2 = -2.125

Simplifying
r2 = -2.125

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
r = {0}

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