(2x+7)x(3x-4)=0

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Solution for (2x+7)x(3x-4)=0 equation: 


Simplifying
(2x + 7) * x(3x + -4) = 0

Reorder the terms:
(7 + 2x) * x(3x + -4) = 0

Reorder the terms:
(7 + 2x) * x(-4 + 3x) = 0

Reorder the terms for easier multiplication:
x(7 + 2x)(-4 + 3x) = 0

Multiply (7 + 2x) * (-4 + 3x)
x(7(-4 + 3x) + 2x * (-4 + 3x)) = 0
x((-4 * 7 + 3x * 7) + 2x * (-4 + 3x)) = 0
x((-28 + 21x) + 2x * (-4 + 3x)) = 0
x(-28 + 21x + (-4 * 2x + 3x * 2x)) = 0
x(-28 + 21x + (-8x + 6x2)) = 0

Combine like terms: 21x + -8x = 13x
x(-28 + 13x + 6x2) = 0
(-28 * x + 13x * x + 6x2 * x) = 0
(-28x + 13x2 + 6x3) = 0

Solving
-28x + 13x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-28 + 13x + 6x2) = 0

Factor a trinomial.
x((-7 + -2x)(4 + -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 '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {0, -3.5, 1.333333333}

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