3r^2+11r+28=10(1-r)

Solution for 3r^2+11r+28=10(1-r) equation:

Simplifying
3r2 + 11r + 28 = 10(1 + -1r)

Reorder the terms:
28 + 11r + 3r2 = 10(1 + -1r)
28 + 11r + 3r2 = (1 * 10 + -1r * 10)
28 + 11r + 3r2 = (10 + -10r)

Solving
28 + 11r + 3r2 = 10 + -10r

Solving for variable 'r'.

Reorder the terms:
28 + -10 + 11r + 10r + 3r2 = 10 + -10r + -10 + 10r

Combine like terms: 28 + -10 = 18
18 + 11r + 10r + 3r2 = 10 + -10r + -10 + 10r

Combine like terms: 11r + 10r = 21r
18 + 21r + 3r2 = 10 + -10r + -10 + 10r

Reorder the terms:
18 + 21r + 3r2 = 10 + -10 + -10r + 10r

Combine like terms: 10 + -10 = 0
18 + 21r + 3r2 = 0 + -10r + 10r
18 + 21r + 3r2 = -10r + 10r

Combine like terms: -10r + 10r = 0
18 + 21r + 3r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + 7r + r2) = 0

Factor a trinomial.
3((6 + r)(1 + r)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(6 + r)' equal to zero and attempt to solve:

Simplifying
6 + r = 0

Solving
6 + r = 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 + r = 0 + -6

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

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

Simplifying
r = -6
Subproblem 2
Set the factor '(1 + r)' equal to zero and attempt to solve:

Simplifying
1 + r = 0

Solving
1 + r = 0

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

Add '-1' to each side of the equation.
1 + -1 + r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + r = 0 + -1
r = 0 + -1

Combine like terms: 0 + -1 = -1
r = -1

Simplifying
r = -1
Solution
r = {-6, -1}