-5k^2+15k=-7k^2+4k-14

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Solution for -5k^2+15k=-7k^2+4k-14 equation: 


Simplifying
-5k2 + 15k = -7k2 + 4k + -14

Reorder the terms:
15k + -5k2 = -7k2 + 4k + -14

Reorder the terms:
15k + -5k2 = -14 + 4k + -7k2

Solving
15k + -5k2 = -14 + 4k + -7k2

Solving for variable 'k'.

Reorder the terms:
14 + 15k + -4k + -5k2 + 7k2 = -14 + 4k + -7k2 + 14 + -4k + 7k2

Combine like terms: 15k + -4k = 11k
14 + 11k + -5k2 + 7k2 = -14 + 4k + -7k2 + 14 + -4k + 7k2

Combine like terms: -5k2 + 7k2 = 2k2
14 + 11k + 2k2 = -14 + 4k + -7k2 + 14 + -4k + 7k2

Reorder the terms:
14 + 11k + 2k2 = -14 + 14 + 4k + -4k + -7k2 + 7k2

Combine like terms: -14 + 14 = 0
14 + 11k + 2k2 = 0 + 4k + -4k + -7k2 + 7k2
14 + 11k + 2k2 = 4k + -4k + -7k2 + 7k2

Combine like terms: 4k + -4k = 0
14 + 11k + 2k2 = 0 + -7k2 + 7k2
14 + 11k + 2k2 = -7k2 + 7k2

Combine like terms: -7k2 + 7k2 = 0
14 + 11k + 2k2 = 0

Factor a trinomial.
(7 + 2k)(2 + k) = 0


Subproblem 1
Set the factor '(7 + 2k)' equal to zero and attempt to solve:

Simplifying
7 + 2k = 0

Solving
7 + 2k = 0

Move all terms containing k to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + 2k = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2k = 0 + -7
2k = 0 + -7

Combine like terms: 0 + -7 = -7
2k = -7

Divide each side by '2'.
k = -3.5

Simplifying
k = -3.5

Subproblem 2
Set the factor '(2 + k)' equal to zero and attempt to solve:

Simplifying
2 + k = 0

Solving
2 + k = 0

Move all terms containing k to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + k = 0 + -2
k = 0 + -2

Combine like terms: 0 + -2 = -2
k = -2

Simplifying
k = -2
Solution
k = {-3.5, -2}

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