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

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

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

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

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

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

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

Solving
-9 + -3x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + -1x + 2x2) = 0

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-1, 1.5}