(8x-10)(5-3x)=0

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Solution for (8x-10)(5-3x)=0 equation: 


Simplifying
(8x + -10)(5 + -3x) = 0

Reorder the terms:
(-10 + 8x)(5 + -3x) = 0

Multiply (-10 + 8x) * (5 + -3x)
(-10(5 + -3x) + 8x * (5 + -3x)) = 0
((5 * -10 + -3x * -10) + 8x * (5 + -3x)) = 0
((-50 + 30x) + 8x * (5 + -3x)) = 0
(-50 + 30x + (5 * 8x + -3x * 8x)) = 0
(-50 + 30x + (40x + -24x2)) = 0

Combine like terms: 30x + 40x = 70x
(-50 + 70x + -24x2) = 0

Solving
-50 + 70x + -24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + 35x + -12x2) = 0

Factor a trinomial.
2((-5 + 3x)(5 + -4x)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {1.666666667, 1.25}

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