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

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

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

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

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

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

Combine like terms: 4r + -3r = 1r
4r(-4 + 1r + 3r2) = 0
(-4 * 4r + 1r * 4r + 3r2 * 4r) = 0
(-16r + 4r2 + 12r3) = 0

Solving
-16r + 4r2 + 12r3 = 0

Solving for variable 'r'.

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

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

Ignore the factor 4.
Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
Subproblem 2
Set the factor '(-4 + -3r)' equal to zero and attempt to solve:

Simplifying
-4 + -3r = 0

Solving
-4 + -3r = 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 + -3r = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3r = 0 + 4
-3r = 0 + 4

Combine like terms: 0 + 4 = 4
-3r = 4

Divide each side by '-3'.
r = -1.333333333

Simplifying
r = -1.333333333
Subproblem 3
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 = {0, -1.333333333, 1}