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

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


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

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

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

Multiply (5 + x) * (-5 + 2x)
(5(-5 + 2x) + x(-5 + 2x)) = 0
((-5 * 5 + 2x * 5) + x(-5 + 2x)) = 0
((-25 + 10x) + x(-5 + 2x)) = 0
(-25 + 10x + (-5 * x + 2x * x)) = 0
(-25 + 10x + (-5x + 2x2)) = 0

Combine like terms: 10x + -5x = 5x
(-25 + 5x + 2x2) = 0

Solving
-25 + 5x + 2x2 = 0

Solving for variable 'x'.

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

Subproblem 1

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

Subproblem 2

Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5

Solution

x = {-5, 2.5}

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