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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-1.666666667, 0.5}

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