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

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


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

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

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

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

Solving
25 + 20x + -5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(5 + 4x + -1x2) = 0

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

Ignore the factor 5.

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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {5, -1}

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