4r^2+58r+180=

Solution for 4r^2+58r+180= equation:

Simplifying
4r2 + 58r + 180 = 0

Reorder the terms:
180 + 58r + 4r2 = 0

Solving
180 + 58r + 4r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(90 + 29r + 2r2) = 0

Factor a trinomial.
2((10 + r)(9 + 2r)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(10 + r)' equal to zero and attempt to solve:

Simplifying
10 + r = 0

Solving
10 + r = 0

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

Add '-10' to each side of the equation.
10 + -10 + r = 0 + -10

Combine like terms: 10 + -10 = 0
0 + r = 0 + -10
r = 0 + -10

Combine like terms: 0 + -10 = -10
r = -10

Simplifying
r = -10
Subproblem 2
Set the factor '(9 + 2r)' equal to zero and attempt to solve:

Simplifying
9 + 2r = 0

Solving
9 + 2r = 0

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

Add '-9' to each side of the equation.
9 + -9 + 2r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2r = 0 + -9
2r = 0 + -9

Combine like terms: 0 + -9 = -9
2r = -9

Divide each side by '2'.
r = -4.5

Simplifying
r = -4.5
Solution
r = {-10, -4.5}