7r^2-4r-3=0

Solution for 7r^2-4r-3=0 equation:

Simplifying
7r2 + -4r + -3 = 0

Reorder the terms:
-3 + -4r + 7r2 = 0

Solving
-3 + -4r + 7r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-3 + -7r)(1 + -1r) = 0

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

Simplifying
1 + -1r = 0

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

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

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

Divide each side by '-1'.
r = 1

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