(2x+4)(5x-1)=0

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Solution for (2x+4)(5x-1)=0 equation:


Simplifying
(2x + 4)(5x + -1) = 0

Reorder the terms:
(4 + 2x)(5x + -1) = 0

Reorder the terms:
(4 + 2x)(-1 + 5x) = 0

Multiply (4 + 2x) * (-1 + 5x)
(4(-1 + 5x) + 2x * (-1 + 5x)) = 0
((-1 * 4 + 5x * 4) + 2x * (-1 + 5x)) = 0
((-4 + 20x) + 2x * (-1 + 5x)) = 0
(-4 + 20x + (-1 * 2x + 5x * 2x)) = 0
(-4 + 20x + (-2x + 10x2)) = 0

Combine like terms: 20x + -2x = 18x
(-4 + 18x + 10x2) = 0

Solving
-4 + 18x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 9x + 5x2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2

Subproblem 2

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 = {-2, 0.2}

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