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

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Solution for (3x-5)(2x+1)=0 equation: 


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

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

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

Multiply (-5 + 3x) * (1 + 2x)
(-5(1 + 2x) + 3x * (1 + 2x)) = 0
((1 * -5 + 2x * -5) + 3x * (1 + 2x)) = 0
((-5 + -10x) + 3x * (1 + 2x)) = 0
(-5 + -10x + (1 * 3x + 2x * 3x)) = 0
(-5 + -10x + (3x + 6x2)) = 0

Combine like terms: -10x + 3x = -7x
(-5 + -7x + 6x2) = 0

Solving
-5 + -7x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -2x)(5 + -3x) = 0


Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve:

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {-0.5, 1.666666667}

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