3x-1=9x(x+1)

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Solution for 3x-1=9x(x+1) equation: 


Simplifying
3x + -1 = 9x(x + 1)

Reorder the terms:
-1 + 3x = 9x(x + 1)

Reorder the terms:
-1 + 3x = 9x(1 + x)
-1 + 3x = (1 * 9x + x * 9x)
-1 + 3x = (9x + 9x2)

Solving
-1 + 3x = 9x + 9x2

Solving for variable 'x'.

Combine like terms: 3x + -9x = -6x
-1 + -6x + -9x2 = 9x + 9x2 + -9x + -9x2

Reorder the terms:
-1 + -6x + -9x2 = 9x + -9x + 9x2 + -9x2

Combine like terms: 9x + -9x = 0
-1 + -6x + -9x2 = 0 + 9x2 + -9x2
-1 + -6x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-1 + -6x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 6x + 9x2) = 0

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

Ignore the factor -1.

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

Simplifying
1 + 3x = 0

Solving
1 + 3x = 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 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

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

Simplifying
1 + 3x = 0

Solving
1 + 3x = 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 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {-0.3333333333, -0.3333333333}

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