2r(4r+5)(r-1)=

Solution for 2r(4r+5)(r-1)= equation:

Simplifying
2r(4r + 5)(r + -1) = 0

Reorder the terms:
2r(5 + 4r)(r + -1) = 0

Reorder the terms:
2r(5 + 4r)(-1 + r) = 0

Multiply (5 + 4r) * (-1 + r)
2r(5(-1 + r) + 4r * (-1 + r)) = 0
2r((-1 * 5 + r * 5) + 4r * (-1 + r)) = 0
2r((-5 + 5r) + 4r * (-1 + r)) = 0
2r(-5 + 5r + (-1 * 4r + r * 4r)) = 0
2r(-5 + 5r + (-4r + 4r2)) = 0

Combine like terms: 5r + -4r = 1r
2r(-5 + 1r + 4r2) = 0
(-5 * 2r + 1r * 2r + 4r2 * 2r) = 0
(-10r + 2r2 + 8r3) = 0

Solving
-10r + 2r2 + 8r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2r'.
2r(-5 + r + 4r2) = 0

Factor a trinomial.
2r((-5 + -4r)(1 + -1r)) = 0

Ignore the factor 2.
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 '(-5 + -4r)' equal to zero and attempt to solve:

Simplifying
-5 + -4r = 0

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

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

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

Divide each side by '-4'.
r = -1.25

Simplifying
r = -1.25
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, -1.25, 1}