7r^2+10r+3=0

Solution for 7r^2+10r+3=0 equation:

Simplifying
7r2 + 10r + 3 = 0

Reorder the terms:
3 + 10r + 7r2 = 0

Solving
3 + 10r + 7r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(1 + r)(3 + 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 '(3 + 7r)' equal to zero and attempt to solve:

Simplifying
3 + 7r = 0

Solving
3 + 7r = 0

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

Add '-3' to each side of the equation.
3 + -3 + 7r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7r = 0 + -3
7r = 0 + -3

Combine like terms: 0 + -3 = -3
7r = -3

Divide each side by '7'.
r = -0.4285714286

Simplifying
r = -0.4285714286
Solution
r = {-1, -0.4285714286}