3(4k+14)=10k-2k(k-7)

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Solution for 3(4k+14)=10k-2k(k-7) equation: 


Simplifying
3(4k + 14) = 10k + -2k(k + -7)

Reorder the terms:
3(14 + 4k) = 10k + -2k(k + -7)
(14 * 3 + 4k * 3) = 10k + -2k(k + -7)
(42 + 12k) = 10k + -2k(k + -7)

Reorder the terms:
42 + 12k = 10k + -2k(-7 + k)
42 + 12k = 10k + (-7 * -2k + k * -2k)
42 + 12k = 10k + (14k + -2k2)

Combine like terms: 10k + 14k = 24k
42 + 12k = 24k + -2k2

Solving
42 + 12k = 24k + -2k2

Solving for variable 'k'.

Combine like terms: 12k + -24k = -12k
42 + -12k + 2k2 = 24k + -2k2 + -24k + 2k2

Reorder the terms:
42 + -12k + 2k2 = 24k + -24k + -2k2 + 2k2

Combine like terms: 24k + -24k = 0
42 + -12k + 2k2 = 0 + -2k2 + 2k2
42 + -12k + 2k2 = -2k2 + 2k2

Combine like terms: -2k2 + 2k2 = 0
42 + -12k + 2k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + -6k + k2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(21 + -6k + k2)' equal to zero and attempt to solve:

Simplifying
21 + -6k + k2 = 0

Solving
21 + -6k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + -6k + -21 + k2 = 0 + -21

Reorder the terms:
21 + -21 + -6k + k2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -6k + k2 = 0 + -21
-6k + k2 = 0 + -21

Combine like terms: 0 + -21 = -21
-6k + k2 = -21

The k term is -6k.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6k + 9 + k2 = -21 + 9

Reorder the terms:
9 + -6k + k2 = -21 + 9

Combine like terms: -21 + 9 = -12
9 + -6k + k2 = -12

Factor a perfect square on the left side:
(k + -3)(k + -3) = -12

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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