(x-5)(5x+8)=0

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Solution for (x-5)(5x+8)=0 equation:


Simplifying
(x + -5)(5x + 8) = 0

Reorder the terms:
(-5 + x)(5x + 8) = 0

Reorder the terms:
(-5 + x)(8 + 5x) = 0

Multiply (-5 + x) * (8 + 5x)
(-5(8 + 5x) + x(8 + 5x)) = 0
((8 * -5 + 5x * -5) + x(8 + 5x)) = 0
((-40 + -25x) + x(8 + 5x)) = 0
(-40 + -25x + (8 * x + 5x * x)) = 0
(-40 + -25x + (8x + 5x2)) = 0

Combine like terms: -25x + 8x = -17x
(-40 + -17x + 5x2) = 0

Solving
-40 + -17x + 5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + -5x)(5 + -1x) = 0

Subproblem 1

Set the factor '(-8 + -5x)' equal to zero and attempt to solve: Simplifying -8 + -5x = 0 Solving -8 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -5x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -5x = 0 + 8 -5x = 0 + 8 Combine like terms: 0 + 8 = 8 -5x = 8 Divide each side by '-5'. x = -1.6 Simplifying x = -1.6

Subproblem 2

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

Solution

x = {-1.6, 5}

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