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

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


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

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

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

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

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

Solving
-2 + 1x + 15x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-0.4, 0.3333333333}

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