7(r-6)=5(r-9)

Solution for 7(r-6)=5(r-9) equation:

Simplifying
7(r + -6) = 5(r + -9)

Reorder the terms:
7(-6 + r) = 5(r + -9)
(-6 * 7 + r * 7) = 5(r + -9)
(-42 + 7r) = 5(r + -9)

Reorder the terms:
-42 + 7r = 5(-9 + r)
-42 + 7r = (-9 * 5 + r * 5)
-42 + 7r = (-45 + 5r)

Solving
-42 + 7r = -45 + 5r

Solving for variable 'r'.

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

Add '-5r' to each side of the equation.
-42 + 7r + -5r = -45 + 5r + -5r

Combine like terms: 7r + -5r = 2r
-42 + 2r = -45 + 5r + -5r

Combine like terms: 5r + -5r = 0
-42 + 2r = -45 + 0
-42 + 2r = -45

Add '42' to each side of the equation.
-42 + 42 + 2r = -45 + 42

Combine like terms: -42 + 42 = 0
0 + 2r = -45 + 42
2r = -45 + 42

Combine like terms: -45 + 42 = -3
2r = -3

Divide each side by '2'.
r = -1.5

Simplifying
r = -1.5