10r^2+15r-2=2r^2

Solution for 10r^2+15r-2=2r^2 equation:

Simplifying
10r2 + 15r + -2 = 2r2

Reorder the terms:
-2 + 15r + 10r2 = 2r2

Solving
-2 + 15r + 10r2 = 2r2

Solving for variable 'r'.

Combine like terms: 10r2 + -2r2 = 8r2
-2 + 15r + 8r2 = 2r2 + -2r2

Combine like terms: 2r2 + -2r2 = 0
-2 + 15r + 8r2 = 0

Factor a trinomial.
(-2 + -1r)(1 + -8r) = 0

Subproblem 1
Set the factor '(-2 + -1r)' equal to zero and attempt to solve:

Simplifying
-2 + -1r = 0

Solving
-2 + -1r = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1r = 0 + 2

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

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

Divide each side by '-1'.
r = -2

Simplifying
r = -2
Subproblem 2
Set the factor '(1 + -8r)' equal to zero and attempt to solve:

Simplifying
1 + -8r = 0

Solving
1 + -8r = 0

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

Add '-1' to each side of the equation.
1 + -1 + -8r = 0 + -1

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

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

Divide each side by '-8'.
r = 0.125

Simplifying
r = 0.125
Solution
r = {-2, 0.125}