(5-x)(2x+3)=0

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Solution for (5-x)(2x+3)=0 equation:


Simplifying
(5 + -1x)(2x + 3) = 0

Reorder the terms:
(5 + -1x)(3 + 2x) = 0

Multiply (5 + -1x) * (3 + 2x)
(5(3 + 2x) + -1x * (3 + 2x)) = 0
((3 * 5 + 2x * 5) + -1x * (3 + 2x)) = 0
((15 + 10x) + -1x * (3 + 2x)) = 0
(15 + 10x + (3 * -1x + 2x * -1x)) = 0
(15 + 10x + (-3x + -2x2)) = 0

Combine like terms: 10x + -3x = 7x
(15 + 7x + -2x2) = 0

Solving
15 + 7x + -2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -1x)(3 + 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 '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5

Solution

x = {5, -1.5}

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