0=(2x-7)(3x+1)

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Solution for 0=(2x-7)(3x+1) equation: 


Simplifying
0 = (2x + -7)(3x + 1)

Reorder the terms:
0 = (-7 + 2x)(3x + 1)

Reorder the terms:
0 = (-7 + 2x)(1 + 3x)

Multiply (-7 + 2x) * (1 + 3x)
0 = (-7(1 + 3x) + 2x * (1 + 3x))
0 = ((1 * -7 + 3x * -7) + 2x * (1 + 3x))
0 = ((-7 + -21x) + 2x * (1 + 3x))
0 = (-7 + -21x + (1 * 2x + 3x * 2x))
0 = (-7 + -21x + (2x + 6x2))

Combine like terms: -21x + 2x = -19x
0 = (-7 + -19x + 6x2)

Solving
0 = -7 + -19x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + 7 = 7
7 + 19x + -6x2 = -7 + -19x + 6x2 + 7 + 19x + -6x2

Reorder the terms:
7 + 19x + -6x2 = -7 + 7 + -19x + 19x + 6x2 + -6x2

Combine like terms: -7 + 7 = 0
7 + 19x + -6x2 = 0 + -19x + 19x + 6x2 + -6x2
7 + 19x + -6x2 = -19x + 19x + 6x2 + -6x2

Combine like terms: -19x + 19x = 0
7 + 19x + -6x2 = 0 + 6x2 + -6x2
7 + 19x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
7 + 19x + -6x2 = 0

Factor a trinomial.
(7 + -2x)(1 + 3x) = 0


Subproblem 1
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5

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 = {3.5, -0.3333333333}

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