6x^2+27x=15

Solution for 6x^2+27x=15 equation:

Simplifying
6x2 + 27x = 15

Reorder the terms:
27x + 6x2 = 15

Solving
27x + 6x2 = 15

Solving for variable 'x'.

Reorder the terms:
-15 + 27x + 6x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + 27x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + 9x + 2x2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

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

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

Divide each side by '-1'.
x = -5

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

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

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

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

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

Simplifying
x = 0.5
Solution
x = {-5, 0.5}