(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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