(3x-5)(2x+4)=0

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Solution for (3x-5)(2x+4)=0 equation: 


Simplifying
(3x + -5)(2x + 4) = 0

Reorder the terms:
(-5 + 3x)(2x + 4) = 0

Reorder the terms:
(-5 + 3x)(4 + 2x) = 0

Multiply (-5 + 3x) * (4 + 2x)
(-5(4 + 2x) + 3x * (4 + 2x)) = 0
((4 * -5 + 2x * -5) + 3x * (4 + 2x)) = 0
((-20 + -10x) + 3x * (4 + 2x)) = 0
(-20 + -10x + (4 * 3x + 2x * 3x)) = 0
(-20 + -10x + (12x + 6x2)) = 0

Combine like terms: -10x + 12x = 2x
(-20 + 2x + 6x2) = 0

Solving
-20 + 2x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + x + 3x2) = 0

Factor a trinomial.
2((-2 + -1x)(5 + -3x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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 = {-2, 1.666666667}

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