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

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


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

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

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

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

Solving for variable 'x'.

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

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

Reorder the terms:
1 + 6x + 9x2 = -1 + 1 + 3x + -3x

Combine like terms: -1 + 1 = 0
1 + 6x + 9x2 = 0 + 3x + -3x
1 + 6x + 9x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
1 + 6x + 9x2 = 0

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


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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