(5x^2-x)(2x+1)=0

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Solution for (5x^2-x)(2x+1)=0 equation:


Simplifying
(5x2 + -1x)(2x + 1) = 0

Reorder the terms:
(-1x + 5x2)(2x + 1) = 0

Reorder the terms:
(-1x + 5x2)(1 + 2x) = 0

Multiply (-1x + 5x2) * (1 + 2x)
(-1x * (1 + 2x) + 5x2 * (1 + 2x)) = 0
((1 * -1x + 2x * -1x) + 5x2 * (1 + 2x)) = 0
((-1x + -2x2) + 5x2 * (1 + 2x)) = 0
(-1x + -2x2 + (1 * 5x2 + 2x * 5x2)) = 0
(-1x + -2x2 + (5x2 + 10x3)) = 0

Combine like terms: -2x2 + 5x2 = 3x2
(-1x + 3x2 + 10x3) = 0

Solving
-1x + 3x2 + 10x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + 3x + 10x2) = 0

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

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 '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5

Subproblem 3

Set the factor '(1 + -5x)' equal to zero and attempt to solve: Simplifying 1 + -5x = 0 Solving 1 + -5x = 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 + -5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x = 0 + -1 -5x = 0 + -1 Combine like terms: 0 + -1 = -1 -5x = -1 Divide each side by '-5'. x = 0.2 Simplifying x = 0.2

Solution

x = {0, -0.5, 0.2}

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