(9x-3)(6x+8)=0

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Solution for (9x-3)(6x+8)=0 equation: 


Simplifying
(9x + -3)(6x + 8) = 0

Reorder the terms:
(-3 + 9x)(6x + 8) = 0

Reorder the terms:
(-3 + 9x)(8 + 6x) = 0

Multiply (-3 + 9x) * (8 + 6x)
(-3(8 + 6x) + 9x * (8 + 6x)) = 0
((8 * -3 + 6x * -3) + 9x * (8 + 6x)) = 0
((-24 + -18x) + 9x * (8 + 6x)) = 0
(-24 + -18x + (8 * 9x + 6x * 9x)) = 0
(-24 + -18x + (72x + 54x2)) = 0

Combine like terms: -18x + 72x = 54x
(-24 + 54x + 54x2) = 0

Solving
-24 + 54x + 54x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-4 + 9x + 9x2) = 0

Factor a trinomial.
6((-4 + -3x)(1 + -3x)) = 0

Ignore the factor 6.

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 '(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 = {-1.333333333, 0.3333333333}

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