7r^2+24r+8=-4-r

Solution for 7r^2+24r+8=-4-r equation:

Simplifying
7r2 + 24r + 8 = -4 + -1r

Reorder the terms:
8 + 24r + 7r2 = -4 + -1r

Solving
8 + 24r + 7r2 = -4 + -1r

Solving for variable 'r'.

Reorder the terms:
8 + 4 + 24r + r + 7r2 = -4 + -1r + 4 + r

Combine like terms: 8 + 4 = 12
12 + 24r + r + 7r2 = -4 + -1r + 4 + r

Combine like terms: 24r + r = 25r
12 + 25r + 7r2 = -4 + -1r + 4 + r

Reorder the terms:
12 + 25r + 7r2 = -4 + 4 + -1r + r

Combine like terms: -4 + 4 = 0
12 + 25r + 7r2 = 0 + -1r + r
12 + 25r + 7r2 = -1r + r

Combine like terms: -1r + r = 0
12 + 25r + 7r2 = 0

Factor a trinomial.
(3 + r)(4 + 7r) = 0

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

Simplifying
3 + r = 0

Solving
3 + r = 0

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

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

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

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

Simplifying
r = -3
Subproblem 2
Set the factor '(4 + 7r)' equal to zero and attempt to solve:

Simplifying
4 + 7r = 0

Solving
4 + 7r = 0

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

Add '-4' to each side of the equation.
4 + -4 + 7r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 7r = 0 + -4
7r = 0 + -4

Combine like terms: 0 + -4 = -4
7r = -4

Divide each side by '7'.
r = -0.5714285714

Simplifying
r = -0.5714285714
Solution
r = {-3, -0.5714285714}