(3x-1)(6x+9)=0

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Solution for (3x-1)(6x+9)=0 equation: 


Simplifying
(3x + -1)(6x + 9) = 0

Reorder the terms:
(-1 + 3x)(6x + 9) = 0

Reorder the terms:
(-1 + 3x)(9 + 6x) = 0

Multiply (-1 + 3x) * (9 + 6x)
(-1(9 + 6x) + 3x * (9 + 6x)) = 0
((9 * -1 + 6x * -1) + 3x * (9 + 6x)) = 0
((-9 + -6x) + 3x * (9 + 6x)) = 0
(-9 + -6x + (9 * 3x + 6x * 3x)) = 0
(-9 + -6x + (27x + 18x2)) = 0

Combine like terms: -6x + 27x = 21x
(-9 + 21x + 18x2) = 0

Solving
-9 + 21x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 7x + 6x2) = 0

Factor a trinomial.
3((-3 + -2x)(1 + -3x)) = 0

Ignore the factor 3.

Subproblem 1
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

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 = {-1.5, 0.3333333333}

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