4k^2-8k-3=-3-5k^2

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

Simplifying
4k2 + -8k + -3 = -3 + -5k2

Reorder the terms:
-3 + -8k + 4k2 = -3 + -5k2

Add '3' to each side of the equation.
-3 + -8k + 3 + 4k2 = -3 + 3 + -5k2

Reorder the terms:
-3 + 3 + -8k + 4k2 = -3 + 3 + -5k2

Combine like terms: -3 + 3 = 0
0 + -8k + 4k2 = -3 + 3 + -5k2
-8k + 4k2 = -3 + 3 + -5k2

Combine like terms: -3 + 3 = 0
-8k + 4k2 = 0 + -5k2
-8k + 4k2 = -5k2

Solving
-8k + 4k2 = -5k2

Solving for variable 'k'.

Combine like terms: 4k2 + 5k2 = 9k2
-8k + 9k2 = -5k2 + 5k2

Combine like terms: -5k2 + 5k2 = 0
-8k + 9k2 = 0

Factor out the Greatest Common Factor (GCF), 'k'.
k(-8 + 9k) = 0

Subproblem 1
Set the factor 'k' equal to zero and attempt to solve:

Simplifying
k = 0

Solving
k = 0

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

Simplifying
k = 0
Subproblem 2
Set the factor '(-8 + 9k)' equal to zero and attempt to solve:

Simplifying
-8 + 9k = 0

Solving
-8 + 9k = 0

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

Add '8' to each side of the equation.
-8 + 8 + 9k = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 9k = 0 + 8
9k = 0 + 8

Combine like terms: 0 + 8 = 8
9k = 8

Divide each side by '9'.
k = 0.8888888889

Simplifying
k = 0.8888888889
Solution
k = {0, 0.8888888889}