6x^2+51x=27

Solution for 6x^2+51x=27 equation:

Simplifying
6x2 + 51x = 27

Reorder the terms:
51x + 6x2 = 27

Solving
51x + 6x2 = 27

Solving for variable 'x'.

Reorder the terms:
-27 + 51x + 6x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + 51x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + 17x + 2x2) = 0

Factor a trinomial.
3((-9 + -1x)(1 + -2x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
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 = {-9, 0.5}