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

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


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

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

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

Combine like terms: 12x + -10x = 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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