4k^2+18k-23=6k-7

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Solution for 4k^2+18k-23=6k-7 equation: 


Simplifying
4k2 + 18k + -23 = 6k + -7

Reorder the terms:
-23 + 18k + 4k2 = 6k + -7

Reorder the terms:
-23 + 18k + 4k2 = -7 + 6k

Solving
-23 + 18k + 4k2 = -7 + 6k

Solving for variable 'k'.

Reorder the terms:
-23 + 7 + 18k + -6k + 4k2 = -7 + 6k + 7 + -6k

Combine like terms: -23 + 7 = -16
-16 + 18k + -6k + 4k2 = -7 + 6k + 7 + -6k

Combine like terms: 18k + -6k = 12k
-16 + 12k + 4k2 = -7 + 6k + 7 + -6k

Reorder the terms:
-16 + 12k + 4k2 = -7 + 7 + 6k + -6k

Combine like terms: -7 + 7 = 0
-16 + 12k + 4k2 = 0 + 6k + -6k
-16 + 12k + 4k2 = 6k + -6k

Combine like terms: 6k + -6k = 0
-16 + 12k + 4k2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + 3k + k2) = 0

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

Ignore the factor 4.

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 + -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
Solution
k = {-4, 1}

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