4r(3r+4)(r-5)=

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Solution for 4r(3r+4)(r-5)= equation: 


Simplifying
4r(3r + 4)(r + -5) = 0

Reorder the terms:
4r(4 + 3r)(r + -5) = 0

Reorder the terms:
4r(4 + 3r)(-5 + r) = 0

Multiply (4 + 3r) * (-5 + r)
4r(4(-5 + r) + 3r * (-5 + r)) = 0
4r((-5 * 4 + r * 4) + 3r * (-5 + r)) = 0
4r((-20 + 4r) + 3r * (-5 + r)) = 0
4r(-20 + 4r + (-5 * 3r + r * 3r)) = 0
4r(-20 + 4r + (-15r + 3r2)) = 0

Combine like terms: 4r + -15r = -11r
4r(-20 + -11r + 3r2) = 0
(-20 * 4r + -11r * 4r + 3r2 * 4r) = 0
(-80r + -44r2 + 12r3) = 0

Solving
-80r + -44r2 + 12r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4r'.
4r(-20 + -11r + 3r2) = 0

Factor a trinomial.
4r((-4 + -3r)(5 + -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 '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {0, -1.333333333, 5}

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