12k-3k(k+5)=48

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Solution for 12k-3k(k+5)=48 equation: 


Simplifying
12k + -3k(k + 5) = 48

Reorder the terms:
12k + -3k(5 + k) = 48
12k + (5 * -3k + k * -3k) = 48
12k + (-15k + -3k2) = 48

Combine like terms: 12k + -15k = -3k
-3k + -3k2 = 48

Solving
-3k + -3k2 = 48

Solving for variable 'k'.

Reorder the terms:
-48 + -3k + -3k2 = 48 + -48

Combine like terms: 48 + -48 = 0
-48 + -3k + -3k2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(16 + k + k2) = 0

Ignore the factor -3.

Subproblem 1
Set the factor '(16 + k + k2)' equal to zero and attempt to solve:

Simplifying
16 + k + k2 = 0

Solving
16 + k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + k + -16 + k2 = 0 + -16

Reorder the terms:
16 + -16 + k + k2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + k + k2 = 0 + -16
k + k2 = 0 + -16

Combine like terms: 0 + -16 = -16
k + k2 = -16

The k term is k.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
k + 0.25 + k2 = -16 + 0.25

Reorder the terms:
0.25 + k + k2 = -16 + 0.25

Combine like terms: -16 + 0.25 = -15.75
0.25 + k + k2 = -15.75

Factor a perfect square on the left side:
(k + 0.5)(k + 0.5) = -15.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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