7r^2-16r-23=1-3r

Solution for 7r^2-16r-23=1-3r equation:

Simplifying
7r2 + -16r + -23 = 1 + -3r

Reorder the terms:
-23 + -16r + 7r2 = 1 + -3r

Solving
-23 + -16r + 7r2 = 1 + -3r

Solving for variable 'r'.

Reorder the terms:
-23 + -1 + -16r + 3r + 7r2 = 1 + -3r + -1 + 3r

Combine like terms: -23 + -1 = -24
-24 + -16r + 3r + 7r2 = 1 + -3r + -1 + 3r

Combine like terms: -16r + 3r = -13r
-24 + -13r + 7r2 = 1 + -3r + -1 + 3r

Reorder the terms:
-24 + -13r + 7r2 = 1 + -1 + -3r + 3r

Combine like terms: 1 + -1 = 0
-24 + -13r + 7r2 = 0 + -3r + 3r
-24 + -13r + 7r2 = -3r + 3r

Combine like terms: -3r + 3r = 0
-24 + -13r + 7r2 = 0

Factor a trinomial.
(-8 + -7r)(3 + -1r) = 0

Subproblem 1
Set the factor '(-8 + -7r)' equal to zero and attempt to solve:

Simplifying
-8 + -7r = 0

Solving
-8 + -7r = 0

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

Add '8' to each side of the equation.
-8 + 8 + -7r = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -7r = 0 + 8
-7r = 0 + 8

Combine like terms: 0 + 8 = 8
-7r = 8

Divide each side by '-7'.
r = -1.142857143

Simplifying
r = -1.142857143
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 = {-1.142857143, 3}