45x^2-14x+1=0

Solution for 45x^2-14x+1=0 equation:

Simplifying
45x2 + -14x + 1 = 0

Reorder the terms:
1 + -14x + 45x2 = 0

Solving
1 + -14x + 45x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -9x)(1 + -5x) = 0

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

Simplifying
1 + -9x = 0

Solving
1 + -9x = 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 + -9x = 0 + -1

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

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

Divide each side by '-9'.
x = 0.1111111111

Simplifying
x = 0.1111111111
Subproblem 2
Set the factor '(1 + -5x)' equal to zero and attempt to solve:

Simplifying
1 + -5x = 0

Solving
1 + -5x = 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 + -5x = 0 + -1

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

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

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

Simplifying
x = 0.2
Solution
x = {0.1111111111, 0.2}