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

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


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

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

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

Multiply (-2 + 5x) * (4 + x)
(-2(4 + x) + 5x * (4 + x)) = 0
((4 * -2 + x * -2) + 5x * (4 + x)) = 0
((-8 + -2x) + 5x * (4 + x)) = 0
(-8 + -2x + (4 * 5x + x * 5x)) = 0
(-8 + -2x + (20x + 5x2)) = 0

Combine like terms: -2x + 20x = 18x
(-8 + 18x + 5x2) = 0

Solving
-8 + 18x + 5x2 = 0

Solving for variable 'x'.

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

Subproblem 1

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

Subproblem 2

Set the factor '(2 + -5x)' equal to zero and attempt to solve: Simplifying 2 + -5x = 0 Solving 2 + -5x = 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 + -5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5x = 0 + -2 -5x = 0 + -2 Combine like terms: 0 + -2 = -2 -5x = -2 Divide each side by '-5'. x = 0.4 Simplifying x = 0.4

Solution

x = {-4, 0.4}

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