5(r+3)-6=3(r-2)-9

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Solution for 5(r+3)-6=3(r-2)-9 equation:


Simplifying
5(r + 3) + -6 = 3(r + -2) + -9

Reorder the terms:
5(3 + r) + -6 = 3(r + -2) + -9
(3 * 5 + r * 5) + -6 = 3(r + -2) + -9
(15 + 5r) + -6 = 3(r + -2) + -9

Reorder the terms:
15 + -6 + 5r = 3(r + -2) + -9

Combine like terms: 15 + -6 = 9
9 + 5r = 3(r + -2) + -9

Reorder the terms:
9 + 5r = 3(-2 + r) + -9
9 + 5r = (-2 * 3 + r * 3) + -9
9 + 5r = (-6 + 3r) + -9

Reorder the terms:
9 + 5r = -6 + -9 + 3r

Combine like terms: -6 + -9 = -15
9 + 5r = -15 + 3r

Solving
9 + 5r = -15 + 3r

Solving for variable 'r'.

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

Add '-3r' to each side of the equation.
9 + 5r + -3r = -15 + 3r + -3r

Combine like terms: 5r + -3r = 2r
9 + 2r = -15 + 3r + -3r

Combine like terms: 3r + -3r = 0
9 + 2r = -15 + 0
9 + 2r = -15

Add '-9' to each side of the equation.
9 + -9 + 2r = -15 + -9

Combine like terms: 9 + -9 = 0
0 + 2r = -15 + -9
2r = -15 + -9

Combine like terms: -15 + -9 = -24
2r = -24

Divide each side by '2'.
r = -12

Simplifying
r = -12

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