(3x+1)(3x-1)=5x-1

Solution for (3x+1)(3x-1)=5x-1 equation:

Simplifying
(3x + 1)(3x + -1) = 5x + -1

Reorder the terms:
(1 + 3x)(3x + -1) = 5x + -1

Reorder the terms:
(1 + 3x)(-1 + 3x) = 5x + -1

Multiply (1 + 3x) * (-1 + 3x)
(1(-1 + 3x) + 3x * (-1 + 3x)) = 5x + -1
((-1 * 1 + 3x * 1) + 3x * (-1 + 3x)) = 5x + -1
((-1 + 3x) + 3x * (-1 + 3x)) = 5x + -1
(-1 + 3x + (-1 * 3x + 3x * 3x)) = 5x + -1
(-1 + 3x + (-3x + 9x2)) = 5x + -1

Combine like terms: 3x + -3x = 0
(-1 + 0 + 9x2) = 5x + -1
(-1 + 9x2) = 5x + -1

Reorder the terms:
-1 + 9x2 = -1 + 5x

Add '1' to each side of the equation.
-1 + 1 + 9x2 = -1 + 1 + 5x

Combine like terms: -1 + 1 = 0
0 + 9x2 = -1 + 1 + 5x
9x2 = -1 + 1 + 5x

Combine like terms: -1 + 1 = 0
9x2 = 0 + 5x
9x2 = 5x

Solving
9x2 = 5x

Solving for variable 'x'.

Reorder the terms:
-5x + 9x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-5x + 9x2 = 0

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

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-5 + 9x)' equal to zero and attempt to solve:

Simplifying
-5 + 9x = 0

Solving
-5 + 9x = 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 + 9x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 9x = 0 + 5
9x = 0 + 5

Combine like terms: 0 + 5 = 5
9x = 5

Divide each side by '9'.
x = 0.5555555556

Simplifying
x = 0.5555555556
Solution
x = {0, 0.5555555556}