(2k^2-k+3)+(5k+3k-7)=0

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Solution for (2k^2-k+3)+(5k+3k-7)=0 equation: 


Simplifying
(2k2 + -1k + 3) + (5k + 3k + -7) = 0

Reorder the terms:
(3 + -1k + 2k2) + (5k + 3k + -7) = 0

Remove parenthesis around (3 + -1k + 2k2)
3 + -1k + 2k2 + (5k + 3k + -7) = 0

Reorder the terms:
3 + -1k + 2k2 + (-7 + 5k + 3k) = 0

Combine like terms: 5k + 3k = 8k
3 + -1k + 2k2 + (-7 + 8k) = 0

Remove parenthesis around (-7 + 8k)
3 + -1k + 2k2 + -7 + 8k = 0

Reorder the terms:
3 + -7 + -1k + 8k + 2k2 = 0

Combine like terms: 3 + -7 = -4
-4 + -1k + 8k + 2k2 = 0

Combine like terms: -1k + 8k = 7k
-4 + 7k + 2k2 = 0

Solving
-4 + 7k + 2k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-4 + -1k)(1 + -2k) = 0


Subproblem 1
Set the factor '(-4 + -1k)' equal to zero and attempt to solve:

Simplifying
-4 + -1k = 0

Solving
-4 + -1k = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1k = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1k = 0 + 4
-1k = 0 + 4

Combine like terms: 0 + 4 = 4
-1k = 4

Divide each side by '-1'.
k = -4

Simplifying
k = -4

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

Simplifying
1 + -2k = 0

Solving
1 + -2k = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2k = 0 + -1
-2k = 0 + -1

Combine like terms: 0 + -1 = -1
-2k = -1

Divide each side by '-2'.
k = 0.5

Simplifying
k = 0.5
Solution
k = {-4, 0.5}

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