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

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


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

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

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

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

Combine like terms: 21x + -2x = 19x
x(-7 + 19x + 6x2) = 0
(-7 * x + 19x * x + 6x2 * x) = 0
(-7x + 19x2 + 6x3) = 0

Solving
-7x + 19x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-7 + 19x + 6x2) = 0

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


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
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 3
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, -3.5, 0.3333333333}

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