(2x-1)(3x+9)=0

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Solution for (2x-1)(3x+9)=0 equation: 


Simplifying
(2x + -1)(3x + 9) = 0

Reorder the terms:
(-1 + 2x)(3x + 9) = 0

Reorder the terms:
(-1 + 2x)(9 + 3x) = 0

Multiply (-1 + 2x) * (9 + 3x)
(-1(9 + 3x) + 2x * (9 + 3x)) = 0
((9 * -1 + 3x * -1) + 2x * (9 + 3x)) = 0
((-9 + -3x) + 2x * (9 + 3x)) = 0
(-9 + -3x + (9 * 2x + 3x * 2x)) = 0
(-9 + -3x + (18x + 6x2)) = 0

Combine like terms: -3x + 18x = 15x
(-9 + 15x + 6x2) = 0

Solving
-9 + 15x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 5x + 2x2) = 0

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

Ignore the factor 3.

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

Simplifying
-3 + -1x = 0

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

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

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

Divide each side by '-1'.
x = -3

Simplifying
x = -3

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-3, 0.5}

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