(6x-5)(2x-9)=0

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Solution for (6x-5)(2x-9)=0 equation: 


Simplifying
(6x + -5)(2x + -9) = 0

Reorder the terms:
(-5 + 6x)(2x + -9) = 0

Reorder the terms:
(-5 + 6x)(-9 + 2x) = 0

Multiply (-5 + 6x) * (-9 + 2x)
(-5(-9 + 2x) + 6x * (-9 + 2x)) = 0
((-9 * -5 + 2x * -5) + 6x * (-9 + 2x)) = 0
((45 + -10x) + 6x * (-9 + 2x)) = 0
(45 + -10x + (-9 * 6x + 2x * 6x)) = 0
(45 + -10x + (-54x + 12x2)) = 0

Combine like terms: -10x + -54x = -64x
(45 + -64x + 12x2) = 0

Solving
45 + -64x + 12x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -6x)(9 + -2x) = 0


Subproblem 1
Set the factor '(5 + -6x)' equal to zero and attempt to solve:

Simplifying
5 + -6x = 0

Solving
5 + -6x = 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 + -6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6x = 0 + -5
-6x = 0 + -5

Combine like terms: 0 + -5 = -5
-6x = -5

Divide each side by '-6'.
x = 0.8333333333

Simplifying
x = 0.8333333333

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 = {0.8333333333, 4.5}

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