(2X-9)(6X+4)=0

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Solution for (2X-9)(6X+4)=0 equation: 


Simplifying
(2X + -9)(6X + 4) = 0

Reorder the terms:
(-9 + 2X)(6X + 4) = 0

Reorder the terms:
(-9 + 2X)(4 + 6X) = 0

Multiply (-9 + 2X) * (4 + 6X)
(-9(4 + 6X) + 2X * (4 + 6X)) = 0
((4 * -9 + 6X * -9) + 2X * (4 + 6X)) = 0
((-36 + -54X) + 2X * (4 + 6X)) = 0
(-36 + -54X + (4 * 2X + 6X * 2X)) = 0
(-36 + -54X + (8X + 12X2)) = 0

Combine like terms: -54X + 8X = -46X
(-36 + -46X + 12X2) = 0

Solving
-36 + -46X + 12X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + -23X + 6X2) = 0

Factor a trinomial.
2((-2 + -3X)(9 + -2X)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(9 + -2X)' equal to zero and attempt to solve:

Simplifying
9 + -2X = 0

Solving
9 + -2X = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2X = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2X = 0 + -9
-2X = 0 + -9

Combine like terms: 0 + -9 = -9
-2X = -9

Divide each side by '-2'.
X = 4.5

Simplifying
X = 4.5
Solution
X = {-0.6666666667, 4.5}

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