(5x^2)(4)+(4x-5)(10x)=0

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Solution for (5x^2)(4)+(4x-5)(10x)=0 equation:


Simplifying
(5x2)(4) + (4x + -5)(10x) = 0

Remove parenthesis around (5x2)
5x2(4) + (4x + -5)(10x) = 0

Reorder the terms for easier multiplication:
5 * 4x2 + (4x + -5)(10x) = 0

Multiply 5 * 4
20x2 + (4x + -5)(10x) = 0

Reorder the terms:
20x2 + (-5 + 4x)(10x) = 0

Remove parenthesis around (10x)
20x2 + (-5 + 4x) * 10x = 0

Reorder the terms for easier multiplication:
20x2 + 10x(-5 + 4x) = 0
20x2 + (-5 * 10x + 4x * 10x) = 0
20x2 + (-50x + 40x2) = 0

Reorder the terms:
-50x + 20x2 + 40x2 = 0

Combine like terms: 20x2 + 40x2 = 60x2
-50x + 60x2 = 0

Solving
-50x + 60x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10x'.
10x(-5 + 6x) = 0

Ignore the factor 10.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(-5 + 6x)' equal to zero and attempt to solve: Simplifying -5 + 6x = 0 Solving -5 + 6x = 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 + 6x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 6x = 0 + 5 6x = 0 + 5 Combine like terms: 0 + 5 = 5 6x = 5 Divide each side by '6'. x = 0.8333333333 Simplifying x = 0.8333333333

Solution

x = {0, 0.8333333333}

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