45x^2+39x=6

Solution for 45x^2+39x=6 equation:

Simplifying
45x2 + 39x = 6

Reorder the terms:
39x + 45x2 = 6

Solving
39x + 45x2 = 6

Solving for variable 'x'.

Reorder the terms:
-6 + 39x + 45x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 39x + 45x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 13x + 15x2) = 0

Factor a trinomial.
3((-1 + -1x)(2 + -15x)) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 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 + -1x = 0 + 1

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(2 + -15x)' equal to zero and attempt to solve:

Simplifying
2 + -15x = 0

Solving
2 + -15x = 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 + -15x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -15x = 0 + -2
-15x = 0 + -2

Combine like terms: 0 + -2 = -2
-15x = -2

Divide each side by '-15'.
x = 0.1333333333

Simplifying
x = 0.1333333333
Solution
x = {-1, 0.1333333333}