75r^2+150r+72=0

Solution for 75r^2+150r+72=0 equation:

Simplifying
75r2 + 150r + 72 = 0

Reorder the terms:
72 + 150r + 75r2 = 0

Solving
72 + 150r + 75r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(24 + 50r + 25r2) = 0

Factor a trinomial.
3((6 + 5r)(4 + 5r)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(6 + 5r)' equal to zero and attempt to solve:

Simplifying
6 + 5r = 0

Solving
6 + 5r = 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 + 5r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5r = 0 + -6
5r = 0 + -6

Combine like terms: 0 + -6 = -6
5r = -6

Divide each side by '5'.
r = -1.2

Simplifying
r = -1.2
Subproblem 2
Set the factor '(4 + 5r)' equal to zero and attempt to solve:

Simplifying
4 + 5r = 0

Solving
4 + 5r = 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 + 5r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5r = 0 + -4
5r = 0 + -4

Combine like terms: 0 + -4 = -4
5r = -4

Divide each side by '5'.
r = -0.8

Simplifying
r = -0.8
Solution
r = {-1.2, -0.8}