2r^2=8r+42

Solution for 2r^2=8r+42 equation:

Simplifying
2r2 = 8r + 42

Reorder the terms:
2r2 = 42 + 8r

Solving
2r2 = 42 + 8r

Solving for variable 'r'.

Reorder the terms:
-42 + -8r + 2r2 = 42 + 8r + -42 + -8r

Reorder the terms:
-42 + -8r + 2r2 = 42 + -42 + 8r + -8r

Combine like terms: 42 + -42 = 0
-42 + -8r + 2r2 = 0 + 8r + -8r
-42 + -8r + 2r2 = 8r + -8r

Combine like terms: 8r + -8r = 0
-42 + -8r + 2r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + -4r + 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}