[4r-(5-2r)]*3-3*(5r+1)=(r-2)*13-12

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Solution for [4r-(5-2r)]*3-3*(5r+1)=(r-2)*13-12 equation:


Simplifying
[4r + -1(5 + -2r)] * 3 + -3(5r + 1) = (r + -2) * 13 + -12
[4r + (5 * -1 + -2r * -1)] * 3 + -3(5r + 1) = (r + -2) * 13 + -12
[4r + (-5 + 2r)] * 3 + -3(5r + 1) = (r + -2) * 13 + -12

Reorder the terms:
[-5 + 4r + 2r] * 3 + -3(5r + 1) = (r + -2) * 13 + -12

Combine like terms: 4r + 2r = 6r
[-5 + 6r] * 3 + -3(5r + 1) = (r + -2) * 13 + -12

Reorder the terms for easier multiplication:
3[-5 + 6r] + -3(5r + 1) = (r + -2) * 13 + -12
[-5 * 3 + 6r * 3] + -3(5r + 1) = (r + -2) * 13 + -12
[-15 + 18r] + -3(5r + 1) = (r + -2) * 13 + -12

Reorder the terms:
-15 + 18r + -3(1 + 5r) = (r + -2) * 13 + -12
-15 + 18r + (1 * -3 + 5r * -3) = (r + -2) * 13 + -12
-15 + 18r + (-3 + -15r) = (r + -2) * 13 + -12

Reorder the terms:
-15 + -3 + 18r + -15r = (r + -2) * 13 + -12

Combine like terms: -15 + -3 = -18
-18 + 18r + -15r = (r + -2) * 13 + -12

Combine like terms: 18r + -15r = 3r
-18 + 3r = (r + -2) * 13 + -12

Reorder the terms:
-18 + 3r = (-2 + r) * 13 + -12

Reorder the terms for easier multiplication:
-18 + 3r = 13(-2 + r) + -12
-18 + 3r = (-2 * 13 + r * 13) + -12
-18 + 3r = (-26 + 13r) + -12

Reorder the terms:
-18 + 3r = -26 + -12 + 13r

Combine like terms: -26 + -12 = -38
-18 + 3r = -38 + 13r

Solving
-18 + 3r = -38 + 13r

Solving for variable 'r'.

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

Add '-13r' to each side of the equation.
-18 + 3r + -13r = -38 + 13r + -13r

Combine like terms: 3r + -13r = -10r
-18 + -10r = -38 + 13r + -13r

Combine like terms: 13r + -13r = 0
-18 + -10r = -38 + 0
-18 + -10r = -38

Add '18' to each side of the equation.
-18 + 18 + -10r = -38 + 18

Combine like terms: -18 + 18 = 0
0 + -10r = -38 + 18
-10r = -38 + 18

Combine like terms: -38 + 18 = -20
-10r = -20

Divide each side by '-10'.
r = 2

Simplifying
r = 2

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