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

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


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

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

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

Reorder the terms for easier multiplication:
x(3 + 2x)(-7 + 3x) = 0

Multiply (3 + 2x) * (-7 + 3x)
x(3(-7 + 3x) + 2x * (-7 + 3x)) = 0
x((-7 * 3 + 3x * 3) + 2x * (-7 + 3x)) = 0
x((-21 + 9x) + 2x * (-7 + 3x)) = 0
x(-21 + 9x + (-7 * 2x + 3x * 2x)) = 0
x(-21 + 9x + (-14x + 6x2)) = 0

Combine like terms: 9x + -14x = -5x
x(-21 + -5x + 6x2) = 0
(-21 * x + -5x * x + 6x2 * x) = 0
(-21x + -5x2 + 6x3) = 0

Solving
-21x + -5x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-21 + -5x + 6x2) = 0

Factor a trinomial.
x((-3 + -2x)(7 + -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 '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 3
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {0, -1.5, 2.333333333}

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