4(k-3)-7=5k(4k-2)

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


Simplifying
4(k + -3) + -7 = 5k(4k + -2)

Reorder the terms:
4(-3 + k) + -7 = 5k(4k + -2)
(-3 * 4 + k * 4) + -7 = 5k(4k + -2)
(-12 + 4k) + -7 = 5k(4k + -2)

Reorder the terms:
-12 + -7 + 4k = 5k(4k + -2)

Combine like terms: -12 + -7 = -19
-19 + 4k = 5k(4k + -2)

Reorder the terms:
-19 + 4k = 5k(-2 + 4k)
-19 + 4k = (-2 * 5k + 4k * 5k)
-19 + 4k = (-10k + 20k2)

Solving
-19 + 4k = -10k + 20k2

Solving for variable 'k'.

Combine like terms: 4k + 10k = 14k
-19 + 14k + -20k2 = -10k + 20k2 + 10k + -20k2

Reorder the terms:
-19 + 14k + -20k2 = -10k + 10k + 20k2 + -20k2

Combine like terms: -10k + 10k = 0
-19 + 14k + -20k2 = 0 + 20k2 + -20k2
-19 + 14k + -20k2 = 20k2 + -20k2

Combine like terms: 20k2 + -20k2 = 0
-19 + 14k + -20k2 = 0

Begin completing the square.  Divide all terms by
-20 the coefficient of the squared term: 

Divide each side by '-20'.
0.95 + -0.7k + k2 = 0

Move the constant term to the right:

Add '-0.95' to each side of the equation.
0.95 + -0.7k + -0.95 + k2 = 0 + -0.95

Reorder the terms:
0.95 + -0.95 + -0.7k + k2 = 0 + -0.95

Combine like terms: 0.95 + -0.95 = 0.00
0.00 + -0.7k + k2 = 0 + -0.95
-0.7k + k2 = 0 + -0.95

Combine like terms: 0 + -0.95 = -0.95
-0.7k + k2 = -0.95

The k term is -0.7k.  Take half its coefficient (-0.35).
Square it (0.1225) and add it to both sides.

Add '0.1225' to each side of the equation.
-0.7k + 0.1225 + k2 = -0.95 + 0.1225

Reorder the terms:
0.1225 + -0.7k + k2 = -0.95 + 0.1225

Combine like terms: -0.95 + 0.1225 = -0.8275
0.1225 + -0.7k + k2 = -0.8275

Factor a perfect square on the left side:
(k + -0.35)(k + -0.35) = -0.8275

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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