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

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


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

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

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

Multiply (1 + 3x) * (-5 + 2x)
(1(-5 + 2x) + 3x * (-5 + 2x)) = 0
((-5 * 1 + 2x * 1) + 3x * (-5 + 2x)) = 0
((-5 + 2x) + 3x * (-5 + 2x)) = 0
(-5 + 2x + (-5 * 3x + 2x * 3x)) = 0
(-5 + 2x + (-15x + 6x2)) = 0

Combine like terms: 2x + -15x = -13x
(-5 + -13x + 6x2) = 0

Solving
-5 + -13x + 6x2 = 0

Solving for variable 'x'.

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


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

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

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 = {-0.3333333333, 2.5}

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