2r^2=20r-42

Solution for 2r^2=20r-42 equation:

Simplifying
2r2 = 20r + -42

Reorder the terms:
2r2 = -42 + 20r

Solving
2r2 = -42 + 20r

Solving for variable 'r'.

Reorder the terms:
42 + -20r + 2r2 = -42 + 20r + 42 + -20r

Reorder the terms:
42 + -20r + 2r2 = -42 + 42 + 20r + -20r

Combine like terms: -42 + 42 = 0
42 + -20r + 2r2 = 0 + 20r + -20r
42 + -20r + 2r2 = 20r + -20r

Combine like terms: 20r + -20r = 0
42 + -20r + 2r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + -10r + r2) = 0

Factor a trinomial.
2((3 + -1r)(7 + -1r)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 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 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Subproblem 2
Set the factor '(7 + -1r)' equal to zero and attempt to solve:

Simplifying
7 + -1r = 0

Solving
7 + -1r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1r = 0 + -7
-1r = 0 + -7

Combine like terms: 0 + -7 = -7
-1r = -7

Divide each side by '-1'.
r = 7

Simplifying
r = 7
Solution
r = {3, 7}