5(3r-2)-4(2r-3)=3(1-2r)

Solution for 5(3r-2)-4(2r-3)=3(1-2r) equation:

Simplifying
5(3r + -2) + -4(2r + -3) = 3(1 + -2r)

Reorder the terms:
5(-2 + 3r) + -4(2r + -3) = 3(1 + -2r)
(-2 * 5 + 3r * 5) + -4(2r + -3) = 3(1 + -2r)
(-10 + 15r) + -4(2r + -3) = 3(1 + -2r)

Reorder the terms:
-10 + 15r + -4(-3 + 2r) = 3(1 + -2r)
-10 + 15r + (-3 * -4 + 2r * -4) = 3(1 + -2r)
-10 + 15r + (12 + -8r) = 3(1 + -2r)

Reorder the terms:
-10 + 12 + 15r + -8r = 3(1 + -2r)

Combine like terms: -10 + 12 = 2
2 + 15r + -8r = 3(1 + -2r)

Combine like terms: 15r + -8r = 7r
2 + 7r = 3(1 + -2r)
2 + 7r = (1 * 3 + -2r * 3)
2 + 7r = (3 + -6r)

Solving
2 + 7r = 3 + -6r

Solving for variable 'r'.

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

Add '6r' to each side of the equation.
2 + 7r + 6r = 3 + -6r + 6r

Combine like terms: 7r + 6r = 13r
2 + 13r = 3 + -6r + 6r

Combine like terms: -6r + 6r = 0
2 + 13r = 3 + 0
2 + 13r = 3

Add '-2' to each side of the equation.
2 + -2 + 13r = 3 + -2

Combine like terms: 2 + -2 = 0
0 + 13r = 3 + -2
13r = 3 + -2

Combine like terms: 3 + -2 = 1
13r = 1

Divide each side by '13'.
r = 0.07692307692

Simplifying
r = 0.07692307692