(3x+7)(2-x)=0

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Solution for (3x+7)(2-x)=0 equation:


Simplifying
(3x + 7)(2 + -1x) = 0

Reorder the terms:
(7 + 3x)(2 + -1x) = 0

Multiply (7 + 3x) * (2 + -1x)
(7(2 + -1x) + 3x * (2 + -1x)) = 0
((2 * 7 + -1x * 7) + 3x * (2 + -1x)) = 0
((14 + -7x) + 3x * (2 + -1x)) = 0
(14 + -7x + (2 * 3x + -1x * 3x)) = 0
(14 + -7x + (6x + -3x2)) = 0

Combine like terms: -7x + 6x = -1x
(14 + -1x + -3x2) = 0

Solving
14 + -1x + -3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -1x)(7 + 3x) = 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 '(7 + 3x)' equal to zero and attempt to solve: Simplifying 7 + 3x = 0 Solving 7 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3x = 0 + -7 3x = 0 + -7 Combine like terms: 0 + -7 = -7 3x = -7 Divide each side by '3'. x = -2.333333333 Simplifying x = -2.333333333

Solution

x = {2, -2.333333333}

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