(x-3)(6x-5)=15

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Solution for (x-3)(6x-5)=15 equation: 


Simplifying
(x + -3)(6x + -5) = 15

Reorder the terms:
(-3 + x)(6x + -5) = 15

Reorder the terms:
(-3 + x)(-5 + 6x) = 15

Multiply (-3 + x) * (-5 + 6x)
(-3(-5 + 6x) + x(-5 + 6x)) = 15
((-5 * -3 + 6x * -3) + x(-5 + 6x)) = 15
((15 + -18x) + x(-5 + 6x)) = 15
(15 + -18x + (-5 * x + 6x * x)) = 15
(15 + -18x + (-5x + 6x2)) = 15

Combine like terms: -18x + -5x = -23x
(15 + -23x + 6x2) = 15

Add '-15' to each side of the equation.
15 + -23x + -15 + 6x2 = 15 + -15

Reorder the terms:
15 + -15 + -23x + 6x2 = 15 + -15

Combine like terms: 15 + -15 = 0
0 + -23x + 6x2 = 15 + -15
-23x + 6x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-23x + 6x2 = 0

Solving
-23x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-23 + 6x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-23 + 6x)' equal to zero and attempt to solve:

Simplifying
-23 + 6x = 0

Solving
-23 + 6x = 0

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

Add '23' to each side of the equation.
-23 + 23 + 6x = 0 + 23

Combine like terms: -23 + 23 = 0
0 + 6x = 0 + 23
6x = 0 + 23

Combine like terms: 0 + 23 = 23
6x = 23

Divide each side by '6'.
x = 3.833333333

Simplifying
x = 3.833333333
Solution
x = {0, 3.833333333}

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