7r^2-19r-14=-3r+1

Solution for 7r^2-19r-14=-3r+1 equation:

Simplifying
7r2 + -19r + -14 = -3r + 1

Reorder the terms:
-14 + -19r + 7r2 = -3r + 1

Reorder the terms:
-14 + -19r + 7r2 = 1 + -3r

Solving
-14 + -19r + 7r2 = 1 + -3r

Solving for variable 'r'.

Reorder the terms:
-14 + -1 + -19r + 3r + 7r2 = 1 + -3r + -1 + 3r

Combine like terms: -14 + -1 = -15
-15 + -19r + 3r + 7r2 = 1 + -3r + -1 + 3r

Combine like terms: -19r + 3r = -16r
-15 + -16r + 7r2 = 1 + -3r + -1 + 3r

Reorder the terms:
-15 + -16r + 7r2 = 1 + -1 + -3r + 3r

Combine like terms: 1 + -1 = 0
-15 + -16r + 7r2 = 0 + -3r + 3r
-15 + -16r + 7r2 = -3r + 3r

Combine like terms: -3r + 3r = 0
-15 + -16r + 7r2 = 0

Factor a trinomial.
(-5 + -7r)(3 + -1r) = 0

Subproblem 1
Set the factor '(-5 + -7r)' equal to zero and attempt to solve:

Simplifying
-5 + -7r = 0

Solving
-5 + -7r = 0

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

Add '5' to each side of the equation.
-5 + 5 + -7r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -7r = 0 + 5
-7r = 0 + 5

Combine like terms: 0 + 5 = 5
-7r = 5

Divide each side by '-7'.
r = -0.7142857143

Simplifying
r = -0.7142857143
Subproblem 2
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 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 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {-0.7142857143, 3}