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

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


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

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

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

Multiply (5 + 4x) * (-1 + 5x)
(5(-1 + 5x) + 4x * (-1 + 5x)) = 0
((-1 * 5 + 5x * 5) + 4x * (-1 + 5x)) = 0
((-5 + 25x) + 4x * (-1 + 5x)) = 0
(-5 + 25x + (-1 * 4x + 5x * 4x)) = 0
(-5 + 25x + (-4x + 20x2)) = 0

Combine like terms: 25x + -4x = 21x
(-5 + 21x + 20x2) = 0

Solving
-5 + 21x + 20x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(-5 + -4x)' equal to zero and attempt to solve: Simplifying -5 + -4x = 0 Solving -5 + -4x = 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 + -4x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4x = 0 + 5 -4x = 0 + 5 Combine like terms: 0 + 5 = 5 -4x = 5 Divide each side by '-4'. x = -1.25 Simplifying x = -1.25

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 = {-1.25, 0.2}

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