4k^2-10k+1=-3

Solution for 4k^2-10k+1=-3 equation:

Simplifying
4k2 + -10k + 1 = -3

Reorder the terms:
1 + -10k + 4k2 = -3

Solving
1 + -10k + 4k2 = -3

Solving for variable 'k'.

Reorder the terms:
1 + 3 + -10k + 4k2 = -3 + 3

Combine like terms: 1 + 3 = 4
4 + -10k + 4k2 = -3 + 3

Combine like terms: -3 + 3 = 0
4 + -10k + 4k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -5k + 2k2) = 0

Factor a trinomial.
2((1 + -2k)(2 + -1k)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -2k)' equal to zero and attempt to solve:

Simplifying
1 + -2k = 0

Solving
1 + -2k = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2k = 0 + -1
-2k = 0 + -1

Combine like terms: 0 + -1 = -1
-2k = -1

Divide each side by '-2'.
k = 0.5

Simplifying
k = 0.5
Subproblem 2
Set the factor '(2 + -1k)' equal to zero and attempt to solve:

Simplifying
2 + -1k = 0

Solving
2 + -1k = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1k = 0 + -2
-1k = 0 + -2

Combine like terms: 0 + -2 = -2
-1k = -2

Divide each side by '-1'.
k = 2

Simplifying
k = 2
Solution
k = {0.5, 2}