3k^2(-2k^2-4k+7)=

Solution for 3k^2(-2k^2-4k+7)= equation:

Simplifying
3k2(-2k2 + -4k + 7) = 0

Reorder the terms:
3k2(7 + -4k + -2k2) = 0
(7 * 3k2 + -4k * 3k2 + -2k2 * 3k2) = 0
(21k2 + -12k3 + -6k4) = 0

Solving
21k2 + -12k3 + -6k4 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3k2'.
3k2(7 + -4k + -2k2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'k2' equal to zero and attempt to solve:

Simplifying
k2 = 0

Solving
k2 = 0

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

Simplifying
k2 = 0

Take the square root of each side:
k = {0}
Subproblem 2
Set the factor '(7 + -4k + -2k2)' equal to zero and attempt to solve:

Simplifying
7 + -4k + -2k2 = 0

Solving
7 + -4k + -2k2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-3.5 + 2k + k2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 2k + 3.5 + k2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 2k + k2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 2k + k2 = 0 + 3.5
2k + k2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
2k + k2 = 3.5

The k term is 2k.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2k + 1 + k2 = 3.5 + 1

Reorder the terms:
1 + 2k + k2 = 3.5 + 1

Combine like terms: 3.5 + 1 = 4.5
1 + 2k + k2 = 4.5

Factor a perfect square on the left side:
(k + 1)(k + 1) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(k + 1) equal to 2.121320344 and -2.121320344.

Subproblem 1
k + 1 = 2.121320344

Simplifying
k + 1 = 2.121320344

Reorder the terms:
1 + k = 2.121320344

Solving
1 + k = 2.121320344

Solving for variable 'k'.

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

Add '-1' to each side of the equation.
1 + -1 + k = 2.121320344 + -1

Combine like terms: 1 + -1 = 0
0 + k = 2.121320344 + -1
k = 2.121320344 + -1

Combine like terms: 2.121320344 + -1 = 1.121320344
k = 1.121320344

Simplifying
k = 1.121320344

Subproblem 2
k + 1 = -2.121320344

Simplifying
k + 1 = -2.121320344

Reorder the terms:
1 + k = -2.121320344

Solving
1 + k = -2.121320344

Solving for variable 'k'.

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

Add '-1' to each side of the equation.
1 + -1 + k = -2.121320344 + -1

Combine like terms: 1 + -1 = 0
0 + k = -2.121320344 + -1
k = -2.121320344 + -1

Combine like terms: -2.121320344 + -1 = -3.121320344
k = -3.121320344

Simplifying
k = -3.121320344

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {1.121320344, -3.121320344}
Solution
k = {0, 1.121320344, -3.121320344}