7(r-5)(4r-1)=0

Solution for 7(r-5)(4r-1)=0 equation:

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

Reorder the terms:
7(-5 + r)(4r + -1) = 0

Reorder the terms:
7(-5 + r)(-1 + 4r) = 0

Multiply (-5 + r) * (-1 + 4r)
7(-5(-1 + 4r) + r(-1 + 4r)) = 0
7((-1 * -5 + 4r * -5) + r(-1 + 4r)) = 0
7((5 + -20r) + r(-1 + 4r)) = 0
7(5 + -20r + (-1 * r + 4r * r)) = 0
7(5 + -20r + (-1r + 4r2)) = 0

Combine like terms: -20r + -1r = -21r
7(5 + -21r + 4r2) = 0
(5 * 7 + -21r * 7 + 4r2 * 7) = 0
(35 + -147r + 28r2) = 0

Solving
35 + -147r + 28r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '7'.
7(5 + -21r + 4r2) = 0

Factor a trinomial.
7((1 + -4r)(5 + -1r)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(1 + -4r)' equal to zero and attempt to solve:

Simplifying
1 + -4r = 0

Solving
1 + -4r = 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 + -4r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4r = 0 + -1
-4r = 0 + -1

Combine like terms: 0 + -1 = -1
-4r = -1

Divide each side by '-4'.
r = 0.25

Simplifying
r = 0.25
Subproblem 2
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 = {0.25, 5}