(2x-3)(6x-5)=0

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Solution for (2x-3)(6x-5)=0 equation: 


Simplifying
(2x + -3)(6x + -5) = 0

Reorder the terms:
(-3 + 2x)(6x + -5) = 0

Reorder the terms:
(-3 + 2x)(-5 + 6x) = 0

Multiply (-3 + 2x) * (-5 + 6x)
(-3(-5 + 6x) + 2x * (-5 + 6x)) = 0
((-5 * -3 + 6x * -3) + 2x * (-5 + 6x)) = 0
((15 + -18x) + 2x * (-5 + 6x)) = 0
(15 + -18x + (-5 * 2x + 6x * 2x)) = 0
(15 + -18x + (-10x + 12x2)) = 0

Combine like terms: -18x + -10x = -28x
(15 + -28x + 12x2) = 0

Solving
15 + -28x + 12x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -6x)(3 + -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 '(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
Solution
x = {0.8333333333, 1.5}

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