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

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


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

Reorder the terms:
5(-2 + k) + -7 = 3k(2k + -3)
(-2 * 5 + k * 5) + -7 = 3k(2k + -3)
(-10 + 5k) + -7 = 3k(2k + -3)

Reorder the terms:
-10 + -7 + 5k = 3k(2k + -3)

Combine like terms: -10 + -7 = -17
-17 + 5k = 3k(2k + -3)

Reorder the terms:
-17 + 5k = 3k(-3 + 2k)
-17 + 5k = (-3 * 3k + 2k * 3k)
-17 + 5k = (-9k + 6k2)

Solving
-17 + 5k = -9k + 6k2

Solving for variable 'k'.

Combine like terms: 5k + 9k = 14k
-17 + 14k + -6k2 = -9k + 6k2 + 9k + -6k2

Reorder the terms:
-17 + 14k + -6k2 = -9k + 9k + 6k2 + -6k2

Combine like terms: -9k + 9k = 0
-17 + 14k + -6k2 = 0 + 6k2 + -6k2
-17 + 14k + -6k2 = 6k2 + -6k2

Combine like terms: 6k2 + -6k2 = 0
-17 + 14k + -6k2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
2.833333333 + -2.333333333k + k2 = 0

Move the constant term to the right:

Add '-2.833333333' to each side of the equation.
2.833333333 + -2.333333333k + -2.833333333 + k2 = 0 + -2.833333333

Reorder the terms:
2.833333333 + -2.833333333 + -2.333333333k + k2 = 0 + -2.833333333

Combine like terms: 2.833333333 + -2.833333333 = 0.000000000
0.000000000 + -2.333333333k + k2 = 0 + -2.833333333
-2.333333333k + k2 = 0 + -2.833333333

Combine like terms: 0 + -2.833333333 = -2.833333333
-2.333333333k + k2 = -2.833333333

The k term is -2.333333333k.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333k + 1.361111112 + k2 = -2.833333333 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333k + k2 = -2.833333333 + 1.361111112

Combine like terms: -2.833333333 + 1.361111112 = -1.472222221
1.361111112 + -2.333333333k + k2 = -1.472222221

Factor a perfect square on the left side:
(k + -1.166666667)(k + -1.166666667) = -1.472222221

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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