2(3x-5)(8-x)=0

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Solution for 2(3x-5)(8-x)=0 equation: 


Simplifying
2(3x + -5)(8 + -1x) = 0

Reorder the terms:
2(-5 + 3x)(8 + -1x) = 0

Multiply (-5 + 3x) * (8 + -1x)
2(-5(8 + -1x) + 3x * (8 + -1x)) = 0
2((8 * -5 + -1x * -5) + 3x * (8 + -1x)) = 0
2((-40 + 5x) + 3x * (8 + -1x)) = 0
2(-40 + 5x + (8 * 3x + -1x * 3x)) = 0
2(-40 + 5x + (24x + -3x2)) = 0

Combine like terms: 5x + 24x = 29x
2(-40 + 29x + -3x2) = 0
(-40 * 2 + 29x * 2 + -3x2 * 2) = 0
(-80 + 58x + -6x2) = 0

Solving
-80 + 58x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-40 + 29x + -3x2) = 0

Factor a trinomial.
2((-8 + x)(5 + -3x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 0

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

Add '8' to each side of the equation.
-8 + 8 + x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + x = 0 + 8
x = 0 + 8

Combine like terms: 0 + 8 = 8
x = 8

Simplifying
x = 8

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 = {8, 1.666666667}

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