5(3-2k)8(3k-4)-4(1+7k)=

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Solution for 5(3-2k)8(3k-4)-4(1+7k)= equation: 


Simplifying
5(3 + -2k) * 8(3k + -4) + -4(1 + 7k) = 0

Reorder the terms:
5(3 + -2k) * 8(-4 + 3k) + -4(1 + 7k) = 0

Reorder the terms for easier multiplication:
5 * 8(3 + -2k)(-4 + 3k) + -4(1 + 7k) = 0

Multiply 5 * 8
40(3 + -2k)(-4 + 3k) + -4(1 + 7k) = 0

Multiply (3 + -2k) * (-4 + 3k)
40(3(-4 + 3k) + -2k * (-4 + 3k)) + -4(1 + 7k) = 0
40((-4 * 3 + 3k * 3) + -2k * (-4 + 3k)) + -4(1 + 7k) = 0
40((-12 + 9k) + -2k * (-4 + 3k)) + -4(1 + 7k) = 0
40(-12 + 9k + (-4 * -2k + 3k * -2k)) + -4(1 + 7k) = 0
40(-12 + 9k + (8k + -6k2)) + -4(1 + 7k) = 0

Combine like terms: 9k + 8k = 17k
40(-12 + 17k + -6k2) + -4(1 + 7k) = 0
(-12 * 40 + 17k * 40 + -6k2 * 40) + -4(1 + 7k) = 0
(-480 + 680k + -240k2) + -4(1 + 7k) = 0
-480 + 680k + -240k2 + (1 * -4 + 7k * -4) = 0
-480 + 680k + -240k2 + (-4 + -28k) = 0

Reorder the terms:
-480 + -4 + 680k + -28k + -240k2 = 0

Combine like terms: -480 + -4 = -484
-484 + 680k + -28k + -240k2 = 0

Combine like terms: 680k + -28k = 652k
-484 + 652k + -240k2 = 0

Solving
-484 + 652k + -240k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-121 + 163k + -60k2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-121 + 163k + -60k2)' equal to zero and attempt to solve:

Simplifying
-121 + 163k + -60k2 = 0

Solving
-121 + 163k + -60k2 = 0

Begin completing the square.  Divide all terms by
-60 the coefficient of the squared term: 

Divide each side by '-60'.
2.016666667 + -2.716666667k + k2 = 0.0

Move the constant term to the right:

Add '-2.016666667' to each side of the equation.
2.016666667 + -2.716666667k + -2.016666667 + k2 = 0.0 + -2.016666667

Reorder the terms:
2.016666667 + -2.016666667 + -2.716666667k + k2 = 0.0 + -2.016666667

Combine like terms: 2.016666667 + -2.016666667 = 0.000000000
0.000000000 + -2.716666667k + k2 = 0.0 + -2.016666667
-2.716666667k + k2 = 0.0 + -2.016666667

Combine like terms: 0.0 + -2.016666667 = -2.016666667
-2.716666667k + k2 = -2.016666667

The k term is -2.716666667k.  Take half its coefficient (-1.358333334).
Square it (1.845069446) and add it to both sides.

Add '1.845069446' to each side of the equation.
-2.716666667k + 1.845069446 + k2 = -2.016666667 + 1.845069446

Reorder the terms:
1.845069446 + -2.716666667k + k2 = -2.016666667 + 1.845069446

Combine like terms: -2.016666667 + 1.845069446 = -0.171597221
1.845069446 + -2.716666667k + k2 = -0.171597221

Factor a perfect square on the left side:
(k + -1.358333334)(k + -1.358333334) = -0.171597221

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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