54x^2+6=39x

Solution for 54x^2+6=39x equation:

Simplifying
54x2 + 6 = 39x

Reorder the terms:
6 + 54x2 = 39x

Solving
6 + 54x2 = 39x

Solving for variable 'x'.

Reorder the terms:
6 + -39x + 54x2 = 39x + -39x

Combine like terms: 39x + -39x = 0
6 + -39x + 54x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -13x + 18x2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -9x)' equal to zero and attempt to solve:

Simplifying
2 + -9x = 0

Solving
2 + -9x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -9x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -9x = 0 + -2
-9x = 0 + -2

Combine like terms: 0 + -2 = -2
-9x = -2

Divide each side by '-9'.
x = 0.2222222222

Simplifying
x = 0.2222222222
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 = {0.2222222222, 0.5}