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

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


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

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

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

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

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

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

Solving for variable 'x'.

Combine like terms: 0 + 5 = 5
5 + 13x + -6x2 = -5 + -13x + 6x2 + 5 + 13x + -6x2

Reorder the terms:
5 + 13x + -6x2 = -5 + 5 + -13x + 13x + 6x2 + -6x2

Combine like terms: -5 + 5 = 0
5 + 13x + -6x2 = 0 + -13x + 13x + 6x2 + -6x2
5 + 13x + -6x2 = -13x + 13x + 6x2 + -6x2

Combine like terms: -13x + 13x = 0
5 + 13x + -6x2 = 0 + 6x2 + -6x2
5 + 13x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
5 + 13x + -6x2 = 0

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


Subproblem 1
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

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 = {2.5, -0.3333333333}

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