(9x-6)(x+1)=0

Solution for (9x-6)(x+1)=0 equation:

Simplifying
(9x + -6)(x + 1) = 0

Reorder the terms:
(-6 + 9x)(x + 1) = 0

Reorder the terms:
(-6 + 9x)(1 + x) = 0

Multiply (-6 + 9x) * (1 + x)
(-6(1 + x) + 9x * (1 + x)) = 0
((1 * -6 + x * -6) + 9x * (1 + x)) = 0
((-6 + -6x) + 9x * (1 + x)) = 0
(-6 + -6x + (1 * 9x + x * 9x)) = 0
(-6 + -6x + (9x + 9x2)) = 0

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

Solving
-6 + 3x + 9x2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
3((-1 + -1x)(2 + -3x)) = 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 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-1, 0.6666666667}