(2x-9)(2+x)=0

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Solution for (2x-9)(2+x)=0 equation:


Simplifying
(2x + -9)(2 + x) = 0

Reorder the terms:
(-9 + 2x)(2 + x) = 0

Multiply (-9 + 2x) * (2 + x)
(-9(2 + x) + 2x * (2 + x)) = 0
((2 * -9 + x * -9) + 2x * (2 + x)) = 0
((-18 + -9x) + 2x * (2 + x)) = 0
(-18 + -9x + (2 * 2x + x * 2x)) = 0
(-18 + -9x + (4x + 2x2)) = 0

Combine like terms: -9x + 4x = -5x
(-18 + -5x + 2x2) = 0

Solving
-18 + -5x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-2 + -1x)(9 + -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 '(9 + -2x)' equal to zero and attempt to solve: Simplifying 9 + -2x = 0 Solving 9 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2x = 0 + -9 -2x = 0 + -9 Combine like terms: 0 + -9 = -9 -2x = -9 Divide each side by '-2'. x = 4.5 Simplifying x = 4.5

Solution

x = {-2, 4.5}

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