10r^2-21r=-4r+6

Solution for 10r^2-21r=-4r+6 equation:

Simplifying
10r2 + -21r = -4r + 6

Reorder the terms:
-21r + 10r2 = -4r + 6

Reorder the terms:
-21r + 10r2 = 6 + -4r

Solving
-21r + 10r2 = 6 + -4r

Solving for variable 'r'.

Reorder the terms:
-6 + -21r + 4r + 10r2 = 6 + -4r + -6 + 4r

Combine like terms: -21r + 4r = -17r
-6 + -17r + 10r2 = 6 + -4r + -6 + 4r

Reorder the terms:
-6 + -17r + 10r2 = 6 + -6 + -4r + 4r

Combine like terms: 6 + -6 = 0
-6 + -17r + 10r2 = 0 + -4r + 4r
-6 + -17r + 10r2 = -4r + 4r

Combine like terms: -4r + 4r = 0
-6 + -17r + 10r2 = 0

Factor a trinomial.
(-3 + -10r)(2 + -1r) = 0

Subproblem 1
Set the factor '(-3 + -10r)' equal to zero and attempt to solve:

Simplifying
-3 + -10r = 0

Solving
-3 + -10r = 0

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

Add '3' to each side of the equation.
-3 + 3 + -10r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -10r = 0 + 3
-10r = 0 + 3

Combine like terms: 0 + 3 = 3
-10r = 3

Divide each side by '-10'.
r = -0.3

Simplifying
r = -0.3
Subproblem 2
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
Solution
r = {-0.3, 2}