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

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


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

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

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

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

Combine like terms: 5x + -6x = -1x
(-2 + -1x + 15x2) = 0

Solving
-2 + -1x + 15x2 = 0

Solving for variable 'x'.

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

Simplifying
2 + -5x = 0

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

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

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

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {-0.3333333333, 0.4}

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