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

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


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

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

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

Multiply (-6 + 2x) * (5 + -3x)
(-6(5 + -3x) + 2x * (5 + -3x)) = 0
((5 * -6 + -3x * -6) + 2x * (5 + -3x)) = 0
((-30 + 18x) + 2x * (5 + -3x)) = 0
(-30 + 18x + (5 * 2x + -3x * 2x)) = 0
(-30 + 18x + (10x + -6x2)) = 0

Combine like terms: 18x + 10x = 28x
(-30 + 28x + -6x2) = 0

Solving
-30 + 28x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 14x + -3x2) = 0

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

Ignore the factor 2.

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

Simplifying
-3 + x = 0

Solving
-3 + x = 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 + x = 0 + 3

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

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

Simplifying
x = 3

Subproblem 2
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
Solution
x = {3, 1.666666667}

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