21r^2+40=-74r-8

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Solution for 21r^2+40=-74r-8 equation: 


Simplifying
21r2 + 40 = -74r + -8

Reorder the terms:
40 + 21r2 = -74r + -8

Reorder the terms:
40 + 21r2 = -8 + -74r

Solving
40 + 21r2 = -8 + -74r

Solving for variable 'r'.

Reorder the terms:
40 + 8 + 74r + 21r2 = -8 + -74r + 8 + 74r

Combine like terms: 40 + 8 = 48
48 + 74r + 21r2 = -8 + -74r + 8 + 74r

Reorder the terms:
48 + 74r + 21r2 = -8 + 8 + -74r + 74r

Combine like terms: -8 + 8 = 0
48 + 74r + 21r2 = 0 + -74r + 74r
48 + 74r + 21r2 = -74r + 74r

Combine like terms: -74r + 74r = 0
48 + 74r + 21r2 = 0

Factor a trinomial.
(8 + 3r)(6 + 7r) = 0


Subproblem 1
Set the factor '(8 + 3r)' equal to zero and attempt to solve:

Simplifying
8 + 3r = 0

Solving
8 + 3r = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3r = 0 + -8
3r = 0 + -8

Combine like terms: 0 + -8 = -8
3r = -8

Divide each side by '3'.
r = -2.666666667

Simplifying
r = -2.666666667

Subproblem 2
Set the factor '(6 + 7r)' equal to zero and attempt to solve:

Simplifying
6 + 7r = 0

Solving
6 + 7r = 0

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

Add '-6' to each side of the equation.
6 + -6 + 7r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 7r = 0 + -6
7r = 0 + -6

Combine like terms: 0 + -6 = -6
7r = -6

Divide each side by '7'.
r = -0.8571428571

Simplifying
r = -0.8571428571
Solution
r = {-2.666666667, -0.8571428571}

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