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

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


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

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

Multiply (-3 + 5x) * (2 + -8x)
(-3(2 + -8x) + 5x * (2 + -8x)) = 0
((2 * -3 + -8x * -3) + 5x * (2 + -8x)) = 0
((-6 + 24x) + 5x * (2 + -8x)) = 0
(-6 + 24x + (2 * 5x + -8x * 5x)) = 0
(-6 + 24x + (10x + -40x2)) = 0

Combine like terms: 24x + 10x = 34x
(-6 + 34x + -40x2) = 0

Solving
-6 + 34x + -40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 17x + -20x2) = 0

Factor a trinomial.
2((-3 + 5x)(1 + -4x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-3 + 5x)' equal to zero and attempt to solve: Simplifying -3 + 5x = 0 Solving -3 + 5x = 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 + 5x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 5x = 0 + 3 5x = 0 + 3 Combine like terms: 0 + 3 = 3 5x = 3 Divide each side by '5'. x = 0.6 Simplifying x = 0.6

Subproblem 2

Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25

Solution

x = {0.6, 0.25}

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