(2x-5)(9x-15)=0

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Solution for (2x-5)(9x-15)=0 equation: 


Simplifying
(2x + -5)(9x + -15) = 0

Reorder the terms:
(-5 + 2x)(9x + -15) = 0

Reorder the terms:
(-5 + 2x)(-15 + 9x) = 0

Multiply (-5 + 2x) * (-15 + 9x)
(-5(-15 + 9x) + 2x * (-15 + 9x)) = 0
((-15 * -5 + 9x * -5) + 2x * (-15 + 9x)) = 0
((75 + -45x) + 2x * (-15 + 9x)) = 0
(75 + -45x + (-15 * 2x + 9x * 2x)) = 0
(75 + -45x + (-30x + 18x2)) = 0

Combine like terms: -45x + -30x = -75x
(75 + -75x + 18x2) = 0

Solving
75 + -75x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(25 + -25x + 6x2) = 0

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

Ignore the factor 3.

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 '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {1.666666667, 2.5}

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