(5+2x)(8-3x)=0

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Solution for (5+2x)(8-3x)=0 equation: 


Simplifying
(5 + 2x)(8 + -3x) = 0

Multiply (5 + 2x) * (8 + -3x)
(5(8 + -3x) + 2x * (8 + -3x)) = 0
((8 * 5 + -3x * 5) + 2x * (8 + -3x)) = 0
((40 + -15x) + 2x * (8 + -3x)) = 0
(40 + -15x + (8 * 2x + -3x * 2x)) = 0
(40 + -15x + (16x + -6x2)) = 0

Combine like terms: -15x + 16x = 1x
(40 + 1x + -6x2) = 0

Solving
40 + 1x + -6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(8 + -3x)(5 + 2x) = 0


Subproblem 1
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667

Subproblem 2
Set the factor '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

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

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {2.666666667, -2.5}

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