4r^2-8r-3=-3+5r^2

Solution for 4r^2-8r-3=-3+5r^2 equation:

Simplifying
4r2 + -8r + -3 = -3 + 5r2

Reorder the terms:
-3 + -8r + 4r2 = -3 + 5r2

Add '3' to each side of the equation.
-3 + -8r + 3 + 4r2 = -3 + 3 + 5r2

Reorder the terms:
-3 + 3 + -8r + 4r2 = -3 + 3 + 5r2

Combine like terms: -3 + 3 = 0
0 + -8r + 4r2 = -3 + 3 + 5r2
-8r + 4r2 = -3 + 3 + 5r2

Combine like terms: -3 + 3 = 0
-8r + 4r2 = 0 + 5r2
-8r + 4r2 = 5r2

Solving
-8r + 4r2 = 5r2

Solving for variable 'r'.

Combine like terms: 4r2 + -5r2 = -1r2
-8r + -1r2 = 5r2 + -5r2

Combine like terms: 5r2 + -5r2 = 0
-8r + -1r2 = 0

Factor out the Greatest Common Factor (GCF), '-1r'.
-1r(8 + r) = 0

Ignore the factor -1.
Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
Subproblem 2
Set the factor '(8 + r)' equal to zero and attempt to solve:

Simplifying
8 + r = 0

Solving
8 + r = 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 + r = 0 + -8

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

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

Simplifying
r = -8
Solution
r = {0, -8}