4r^2+20r+14=-2

Solution for 4r^2+20r+14=-2 equation:

Simplifying
4r2 + 20r + 14 = -2

Reorder the terms:
14 + 20r + 4r2 = -2

Solving
14 + 20r + 4r2 = -2

Solving for variable 'r'.

Reorder the terms:
14 + 2 + 20r + 4r2 = -2 + 2

Combine like terms: 14 + 2 = 16
16 + 20r + 4r2 = -2 + 2

Combine like terms: -2 + 2 = 0
16 + 20r + 4r2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + 5r + r2) = 0

Factor a trinomial.
4((4 + r)(1 + r)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(4 + r)' equal to zero and attempt to solve:

Simplifying
4 + r = 0

Solving
4 + r = 0

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

Add '-4' to each side of the equation.
4 + -4 + r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + r = 0 + -4
r = 0 + -4

Combine like terms: 0 + -4 = -4
r = -4

Simplifying
r = -4
Subproblem 2
Set the factor '(1 + r)' equal to zero and attempt to solve:

Simplifying
1 + r = 0

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

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

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

Simplifying
r = -1
Solution
r = {-4, -1}