4r^2+10r+1=-3

Solution for 4r^2+10r+1=-3 equation:

Simplifying
4r2 + 10r + 1 = -3

Reorder the terms:
1 + 10r + 4r2 = -3

Solving
1 + 10r + 4r2 = -3

Solving for variable 'r'.

Reorder the terms:
1 + 3 + 10r + 4r2 = -3 + 3

Combine like terms: 1 + 3 = 4
4 + 10r + 4r2 = -3 + 3

Combine like terms: -3 + 3 = 0
4 + 10r + 4r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 5r + 2r2) = 0

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

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

Simplifying
2 + r = 0

Solving
2 + r = 0

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

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

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

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

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

Simplifying
1 + 2r = 0

Solving
1 + 2r = 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 + 2r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2r = 0 + -1
2r = 0 + -1

Combine like terms: 0 + -1 = -1
2r = -1

Divide each side by '2'.
r = -0.5

Simplifying
r = -0.5
Solution
r = {-2, -0.5}