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

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

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

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

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

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

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

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

Solving
-8k + 4k2 = -5k

Solving for variable 'k'.

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

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

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

Factor out the Greatest Common Factor (GCF), 'k'.
k(-3 + 4k) = 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 '(-3 + 4k)' equal to zero and attempt to solve:

Simplifying
-3 + 4k = 0

Solving
-3 + 4k = 0

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

Add '3' to each side of the equation.
-3 + 3 + 4k = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 4k = 0 + 3
4k = 0 + 3

Combine like terms: 0 + 3 = 3
4k = 3

Divide each side by '4'.
k = 0.75

Simplifying
k = 0.75
Solution
k = {0, 0.75}