2(5r-5)4(r-3)=

Solution for 2(5r-5)4(r-3)= equation:

Simplifying
2(5r + -5) * 4(r + -3) = 0

Reorder the terms:
2(-5 + 5r) * 4(r + -3) = 0

Reorder the terms:
2(-5 + 5r) * 4(-3 + r) = 0

Reorder the terms for easier multiplication:
2 * 4(-5 + 5r)(-3 + r) = 0

Multiply 2 * 4
8(-5 + 5r)(-3 + r) = 0

Multiply (-5 + 5r) * (-3 + r)
8(-5(-3 + r) + 5r * (-3 + r)) = 0
8((-3 * -5 + r * -5) + 5r * (-3 + r)) = 0
8((15 + -5r) + 5r * (-3 + r)) = 0
8(15 + -5r + (-3 * 5r + r * 5r)) = 0
8(15 + -5r + (-15r + 5r2)) = 0

Combine like terms: -5r + -15r = -20r
8(15 + -20r + 5r2) = 0
(15 * 8 + -20r * 8 + 5r2 * 8) = 0
(120 + -160r + 40r2) = 0

Solving
120 + -160r + 40r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '40'.
40(3 + -4r + r2) = 0

Factor a trinomial.
40((1 + -1r)(3 + -1r)) = 0

Ignore the factor 40.
Subproblem 1
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
Subproblem 2
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
Solution
r = {1, 3}