4(r+3)(r-1)=0

Solution for 4(r+3)(r-1)=0 equation:

Simplifying
4(r + 3)(r + -1) = 0

Reorder the terms:
4(3 + r)(r + -1) = 0

Reorder the terms:
4(3 + r)(-1 + r) = 0

Multiply (3 + r) * (-1 + r)
4(3(-1 + r) + r(-1 + r)) = 0
4((-1 * 3 + r * 3) + r(-1 + r)) = 0
4((-3 + 3r) + r(-1 + r)) = 0
4(-3 + 3r + (-1 * r + r * r)) = 0
4(-3 + 3r + (-1r + r2)) = 0

Combine like terms: 3r + -1r = 2r
4(-3 + 2r + r2) = 0
(-3 * 4 + 2r * 4 + r2 * 4) = 0
(-12 + 8r + 4r2) = 0

Solving
-12 + 8r + 4r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + 2r + r2) = 0

Factor a trinomial.
4((-3 + -1r)(1 + -1r)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-3 + -1r)' equal to zero and attempt to solve:

Simplifying
-3 + -1r = 0

Solving
-3 + -1r = 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 + -1r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1r = 0 + 3
-1r = 0 + 3

Combine like terms: 0 + 3 = 3
-1r = 3

Divide each side by '-1'.
r = -3

Simplifying
r = -3
Subproblem 2
Set the factor '(1 + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1r = 0

Solving
1 + -1r = 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 + -1r = 0 + -1

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

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

Divide each side by '-1'.
r = 1

Simplifying
r = 1
Solution
r = {-3, 1}