2r^2-12r=-7r

Solution for 2r^2-12r=-7r equation:

Simplifying
2r2 + -12r = -7r

Reorder the terms:
-12r + 2r2 = -7r

Solving
-12r + 2r2 = -7r

Solving for variable 'r'.

Reorder the terms:
-12r + 7r + 2r2 = -7r + 7r

Combine like terms: -12r + 7r = -5r
-5r + 2r2 = -7r + 7r

Combine like terms: -7r + 7r = 0
-5r + 2r2 = 0

Factor out the Greatest Common Factor (GCF), 'r'.
r(-5 + 2r) = 0

Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
Subproblem 2
Set the factor '(-5 + 2r)' equal to zero and attempt to solve:

Simplifying
-5 + 2r = 0

Solving
-5 + 2r = 0

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

Add '5' to each side of the equation.
-5 + 5 + 2r = 0 + 5

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

Combine like terms: 0 + 5 = 5
2r = 5

Divide each side by '2'.
r = 2.5

Simplifying
r = 2.5
Solution
r = {0, 2.5}