(6x-9)(3x+4)=0

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Solution for (6x-9)(3x+4)=0 equation: 


Simplifying
(6x + -9)(3x + 4) = 0

Reorder the terms:
(-9 + 6x)(3x + 4) = 0

Reorder the terms:
(-9 + 6x)(4 + 3x) = 0

Multiply (-9 + 6x) * (4 + 3x)
(-9(4 + 3x) + 6x * (4 + 3x)) = 0
((4 * -9 + 3x * -9) + 6x * (4 + 3x)) = 0
((-36 + -27x) + 6x * (4 + 3x)) = 0
(-36 + -27x + (4 * 6x + 3x * 6x)) = 0
(-36 + -27x + (24x + 18x2)) = 0

Combine like terms: -27x + 24x = -3x
(-36 + -3x + 18x2) = 0

Solving
-36 + -3x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + -1x + 6x2) = 0

Factor a trinomial.
3((-4 + -3x)(3 + -2x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

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 = {-1.333333333, 1.5}

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