(6k+7)(k-2)=12k

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Solution for (6k+7)(k-2)=12k equation: 


Simplifying
(6k + 7)(k + -2) = 12k

Reorder the terms:
(7 + 6k)(k + -2) = 12k

Reorder the terms:
(7 + 6k)(-2 + k) = 12k

Multiply (7 + 6k) * (-2 + k)
(7(-2 + k) + 6k * (-2 + k)) = 12k
((-2 * 7 + k * 7) + 6k * (-2 + k)) = 12k
((-14 + 7k) + 6k * (-2 + k)) = 12k
(-14 + 7k + (-2 * 6k + k * 6k)) = 12k
(-14 + 7k + (-12k + 6k2)) = 12k

Combine like terms: 7k + -12k = -5k
(-14 + -5k + 6k2) = 12k

Solving
-14 + -5k + 6k2 = 12k

Solving for variable 'k'.

Reorder the terms:
-14 + -5k + -12k + 6k2 = 12k + -12k

Combine like terms: -5k + -12k = -17k
-14 + -17k + 6k2 = 12k + -12k

Combine like terms: 12k + -12k = 0
-14 + -17k + 6k2 = 0

Factor a trinomial.
(-2 + -3k)(7 + -2k) = 0


Subproblem 1
Set the factor '(-2 + -3k)' equal to zero and attempt to solve:

Simplifying
-2 + -3k = 0

Solving
-2 + -3k = 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 + -3k = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3k = 0 + 2
-3k = 0 + 2

Combine like terms: 0 + 2 = 2
-3k = 2

Divide each side by '-3'.
k = -0.6666666667

Simplifying
k = -0.6666666667

Subproblem 2
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
Solution
k = {-0.6666666667, 3.5}

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