15k^2+27k-5=1

Solution for 15k^2+27k-5=1 equation:

Simplifying
15k2 + 27k + -5 = 1

Reorder the terms:
-5 + 27k + 15k2 = 1

Solving
-5 + 27k + 15k2 = 1

Solving for variable 'k'.

Reorder the terms:
-5 + -1 + 27k + 15k2 = 1 + -1

Combine like terms: -5 + -1 = -6
-6 + 27k + 15k2 = 1 + -1

Combine like terms: 1 + -1 = 0
-6 + 27k + 15k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 9k + 5k2) = 0

Factor a trinomial.
3((-2 + -1k)(1 + -5k)) = 0

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

Simplifying
-2 + -1k = 0

Solving
-2 + -1k = 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 + -1k = 0 + 2

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

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

Divide each side by '-1'.
k = -2

Simplifying
k = -2
Subproblem 2
Set the factor '(1 + -5k)' equal to zero and attempt to solve:

Simplifying
1 + -5k = 0

Solving
1 + -5k = 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 + -5k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5k = 0 + -1
-5k = 0 + -1

Combine like terms: 0 + -1 = -1
-5k = -1

Divide each side by '-5'.
k = 0.2

Simplifying
k = 0.2
Solution
k = {-2, 0.2}