5r^2+4r+2=3

Solution for 5r^2+4r+2=3 equation:

Simplifying
5r2 + 4r + 2 = 3

Reorder the terms:
2 + 4r + 5r2 = 3

Solving
2 + 4r + 5r2 = 3

Solving for variable 'r'.

Reorder the terms:
2 + -3 + 4r + 5r2 = 3 + -3

Combine like terms: 2 + -3 = -1
-1 + 4r + 5r2 = 3 + -3

Combine like terms: 3 + -3 = 0
-1 + 4r + 5r2 = 0

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

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

Simplifying
-1 + -1r = 0

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

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

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

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

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

Simplifying
1 + -5r = 0

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

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

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

Divide each side by '-5'.
r = 0.2

Simplifying
r = 0.2
Solution
r = {-1, 0.2}