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

Subproblem 1

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

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 = {-2.5, 5}

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