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

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


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

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

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

Multiply (-4 + 6x) * (9 + 6x)
(-4(9 + 6x) + 6x * (9 + 6x)) = 0
((9 * -4 + 6x * -4) + 6x * (9 + 6x)) = 0
((-36 + -24x) + 6x * (9 + 6x)) = 0
(-36 + -24x + (9 * 6x + 6x * 6x)) = 0
(-36 + -24x + (54x + 36x2)) = 0

Combine like terms: -24x + 54x = 30x
(-36 + 30x + 36x2) = 0

Solving
-36 + 30x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-6 + 5x + 6x2) = 0

Factor a trinomial.
6((-3 + -2x)(2 + -3x)) = 0

Ignore the factor 6.

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 '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

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

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-1.5, 0.6666666667}

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