3r^2=-144-42r

Solution for 3r^2=-144-42r equation:

Simplifying
3r2 = -144 + -42r

Solving
3r2 = -144 + -42r

Solving for variable 'r'.

Reorder the terms:
144 + 42r + 3r2 = -144 + -42r + 144 + 42r

Reorder the terms:
144 + 42r + 3r2 = -144 + 144 + -42r + 42r

Combine like terms: -144 + 144 = 0
144 + 42r + 3r2 = 0 + -42r + 42r
144 + 42r + 3r2 = -42r + 42r

Combine like terms: -42r + 42r = 0
144 + 42r + 3r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(48 + 14r + r2) = 0

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

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

Simplifying
8 + r = 0

Solving
8 + r = 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 + r = 0 + -8

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

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

Simplifying
r = -8
Subproblem 2
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
Solution
r = {-8, -6}