10k^2-12=-5k-7

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Solution for 10k^2-12=-5k-7 equation: 


Simplifying
10k2 + -12 = -5k + -7

Reorder the terms:
-12 + 10k2 = -5k + -7

Reorder the terms:
-12 + 10k2 = -7 + -5k

Solving
-12 + 10k2 = -7 + -5k

Solving for variable 'k'.

Reorder the terms:
-12 + 7 + 5k + 10k2 = -7 + -5k + 7 + 5k

Combine like terms: -12 + 7 = -5
-5 + 5k + 10k2 = -7 + -5k + 7 + 5k

Reorder the terms:
-5 + 5k + 10k2 = -7 + 7 + -5k + 5k

Combine like terms: -7 + 7 = 0
-5 + 5k + 10k2 = 0 + -5k + 5k
-5 + 5k + 10k2 = -5k + 5k

Combine like terms: -5k + 5k = 0
-5 + 5k + 10k2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + k + 2k2) = 0

Factor a trinomial.
5((-1 + -1k)(1 + -2k)) = 0

Ignore the factor 5.

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

Simplifying
-1 + -1k = 0

Solving
-1 + -1k = 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 + -1k = 0 + 1

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

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

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

Simplifying
k = -1

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 = {-1, 0.5}

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