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

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


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

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

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

Combine like terms: -2x + 15x = 13x
(10 + 13x + -3x2) = 0

Solving
10 + 13x + -3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -1x)(2 + 3x) = 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 '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {5, -0.6666666667}

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