7(r-3)-6(r-1)=2(r+4)

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Solution for 7(r-3)-6(r-1)=2(r+4) equation:


Simplifying
7(r + -3) + -6(r + -1) = 2(r + 4)

Reorder the terms:
7(-3 + r) + -6(r + -1) = 2(r + 4)
(-3 * 7 + r * 7) + -6(r + -1) = 2(r + 4)
(-21 + 7r) + -6(r + -1) = 2(r + 4)

Reorder the terms:
-21 + 7r + -6(-1 + r) = 2(r + 4)
-21 + 7r + (-1 * -6 + r * -6) = 2(r + 4)
-21 + 7r + (6 + -6r) = 2(r + 4)

Reorder the terms:
-21 + 6 + 7r + -6r = 2(r + 4)

Combine like terms: -21 + 6 = -15
-15 + 7r + -6r = 2(r + 4)

Combine like terms: 7r + -6r = 1r
-15 + 1r = 2(r + 4)

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

Solving
-15 + 1r = 8 + 2r

Solving for variable 'r'.

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

Add '-2r' to each side of the equation.
-15 + 1r + -2r = 8 + 2r + -2r

Combine like terms: 1r + -2r = -1r
-15 + -1r = 8 + 2r + -2r

Combine like terms: 2r + -2r = 0
-15 + -1r = 8 + 0
-15 + -1r = 8

Add '15' to each side of the equation.
-15 + 15 + -1r = 8 + 15

Combine like terms: -15 + 15 = 0
0 + -1r = 8 + 15
-1r = 8 + 15

Combine like terms: 8 + 15 = 23
-1r = 23

Divide each side by '-1'.
r = -23

Simplifying
r = -23

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