2(3x-5)(4x-9)=0

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Solution for 2(3x-5)(4x-9)=0 equation: 


Simplifying
2(3x + -5)(4x + -9) = 0

Reorder the terms:
2(-5 + 3x)(4x + -9) = 0

Reorder the terms:
2(-5 + 3x)(-9 + 4x) = 0

Multiply (-5 + 3x) * (-9 + 4x)
2(-5(-9 + 4x) + 3x * (-9 + 4x)) = 0
2((-9 * -5 + 4x * -5) + 3x * (-9 + 4x)) = 0
2((45 + -20x) + 3x * (-9 + 4x)) = 0
2(45 + -20x + (-9 * 3x + 4x * 3x)) = 0
2(45 + -20x + (-27x + 12x2)) = 0

Combine like terms: -20x + -27x = -47x
2(45 + -47x + 12x2) = 0
(45 * 2 + -47x * 2 + 12x2 * 2) = 0
(90 + -94x + 24x2) = 0

Solving
90 + -94x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(45 + -47x + 12x2) = 0

Factor a trinomial.
2((5 + -3x)(9 + -4x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667

Subproblem 2
Set the factor '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 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 + -4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4x = 0 + -9
-4x = 0 + -9

Combine like terms: 0 + -9 = -9
-4x = -9

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25
Solution
x = {1.666666667, 2.25}

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