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

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


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

Reorder the terms:
(5 + 2x)(2 + -1x) = 0

Multiply (5 + 2x) * (2 + -1x)
(5(2 + -1x) + 2x * (2 + -1x)) = 0
((2 * 5 + -1x * 5) + 2x * (2 + -1x)) = 0
((10 + -5x) + 2x * (2 + -1x)) = 0
(10 + -5x + (2 * 2x + -1x * 2x)) = 0
(10 + -5x + (4x + -2x2)) = 0

Combine like terms: -5x + 4x = -1x
(10 + -1x + -2x2) = 0

Solving
10 + -1x + -2x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

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 = {2, -2.5}

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