4r^2-90=2r

Solution for 4r^2-90=2r equation:

Simplifying
4r2 + -90 = 2r

Reorder the terms:
-90 + 4r2 = 2r

Solving
-90 + 4r2 = 2r

Solving for variable 'r'.

Reorder the terms:
-90 + -2r + 4r2 = 2r + -2r

Combine like terms: 2r + -2r = 0
-90 + -2r + 4r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + -1r + 2r2) = 0

Factor a trinomial.
2((-9 + -2r)(5 + -1r)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + -2r)' equal to zero and attempt to solve:

Simplifying
-9 + -2r = 0

Solving
-9 + -2r = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2r = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2r = 0 + 9
-2r = 0 + 9

Combine like terms: 0 + 9 = 9
-2r = 9

Divide each side by '-2'.
r = -4.5

Simplifying
r = -4.5
Subproblem 2
Set the factor '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 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 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {-4.5, 5}