7r^2+11r+4=0

Solution for 7r^2+11r+4=0 equation:

Simplifying
7r2 + 11r + 4 = 0

Reorder the terms:
4 + 11r + 7r2 = 0

Solving
4 + 11r + 7r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(1 + r)(4 + 7r) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + 7r)' equal to zero and attempt to solve:

Simplifying
4 + 7r = 0

Solving
4 + 7r = 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 + 7r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 7r = 0 + -4
7r = 0 + -4

Combine like terms: 0 + -4 = -4
7r = -4

Divide each side by '7'.
r = -0.5714285714

Simplifying
r = -0.5714285714
Solution
r = {-1, -0.5714285714}