4r(5t-10)-1rt=5r(3t-6)

Solution for 4r(5t-10)-1rt=5r(3t-6) equation:

Simplifying
4r(5t + -10) + -1rt = 5r(3t + -6)

Reorder the terms:
4r(-10 + 5t) + -1rt = 5r(3t + -6)
(-10 * 4r + 5t * 4r) + -1rt = 5r(3t + -6)
(-40r + 20rt) + -1rt = 5r(3t + -6)

Combine like terms: 20rt + -1rt = 19rt
-40r + 19rt = 5r(3t + -6)

Reorder the terms:
-40r + 19rt = 5r(-6 + 3t)
-40r + 19rt = (-6 * 5r + 3t * 5r)
-40r + 19rt = (-30r + 15rt)

Solving
-40r + 19rt = -30r + 15rt

Solving for variable 'r'.

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

Add '30r' to each side of the equation.
-40r + 30r + 19rt = -30r + 30r + 15rt

Combine like terms: -40r + 30r = -10r
-10r + 19rt = -30r + 30r + 15rt

Combine like terms: -30r + 30r = 0
-10r + 19rt = 0 + 15rt
-10r + 19rt = 15rt

Add '-15rt' to each side of the equation.
-10r + 19rt + -15rt = 15rt + -15rt

Combine like terms: 19rt + -15rt = 4rt
-10r + 4rt = 15rt + -15rt

Combine like terms: 15rt + -15rt = 0
-10r + 4rt = 0

Factor out the Greatest Common Factor (GCF), '2r'.
2r(-5 + 2t) = 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 + 2t)' equal to zero and attempt to solve:

Simplifying
-5 + 2t = 0

Solving
-5 + 2t = 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 + 2t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2t = 0 + 5
2t = 0 + 5

Combine like terms: 0 + 5 = 5
2t = 5

Add '-2t' to each side of the equation.
2t + -2t = 5 + -2t

Combine like terms: 2t + -2t = 0
0 = 5 + -2t

Simplifying
0 = 5 + -2t

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
r = {0}