5r^2+23r+21=

Solution for 5r^2+23r+21= equation:

Simplifying
5r2 + 23r + 21 = 0

Reorder the terms:
21 + 23r + 5r2 = 0

Solving
21 + 23r + 5r2 = 0

Solving for variable 'r'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
4.2 + 4.6r + r2 = 0

Move the constant term to the right:

Add '-4.2' to each side of the equation.
4.2 + 4.6r + -4.2 + r2 = 0 + -4.2

Reorder the terms:
4.2 + -4.2 + 4.6r + r2 = 0 + -4.2

Combine like terms: 4.2 + -4.2 = 0.0
0.0 + 4.6r + r2 = 0 + -4.2
4.6r + r2 = 0 + -4.2

Combine like terms: 0 + -4.2 = -4.2
4.6r + r2 = -4.2

The r term is 4.6r.  Take half its coefficient (2.3).
Square it (5.29) and add it to both sides.

Add '5.29' to each side of the equation.
4.6r + 5.29 + r2 = -4.2 + 5.29

Reorder the terms:
5.29 + 4.6r + r2 = -4.2 + 5.29

Combine like terms: -4.2 + 5.29 = 1.09
5.29 + 4.6r + r2 = 1.09

Factor a perfect square on the left side:
(r + 2.3)(r + 2.3) = 1.09

Calculate the square root of the right side: 1.044030651

Break this problem into two subproblems by setting 
(r + 2.3) equal to 1.044030651 and -1.044030651.

Subproblem 1
r + 2.3 = 1.044030651

Simplifying
r + 2.3 = 1.044030651

Reorder the terms:
2.3 + r = 1.044030651

Solving
2.3 + r = 1.044030651

Solving for variable 'r'.

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

Add '-2.3' to each side of the equation.
2.3 + -2.3 + r = 1.044030651 + -2.3

Combine like terms: 2.3 + -2.3 = 0.0
0.0 + r = 1.044030651 + -2.3
r = 1.044030651 + -2.3

Combine like terms: 1.044030651 + -2.3 = -1.255969349
r = -1.255969349

Simplifying
r = -1.255969349

Subproblem 2
r + 2.3 = -1.044030651

Simplifying
r + 2.3 = -1.044030651

Reorder the terms:
2.3 + r = -1.044030651

Solving
2.3 + r = -1.044030651

Solving for variable 'r'.

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

Add '-2.3' to each side of the equation.
2.3 + -2.3 + r = -1.044030651 + -2.3

Combine like terms: 2.3 + -2.3 = 0.0
0.0 + r = -1.044030651 + -2.3
r = -1.044030651 + -2.3

Combine like terms: -1.044030651 + -2.3 = -3.344030651
r = -3.344030651

Simplifying
r = -3.344030651

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-1.255969349, -3.344030651}