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

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


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

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

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

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

Combine like terms: -4x + 21x = 17x
x(-28 + 17x + 3x2) = 0
(-28 * x + 17x * x + 3x2 * x) = 0
(-28x + 17x2 + 3x3) = 0

Solving
-28x + 17x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-28 + 17x + 3x2) = 0

Factor a trinomial.
x((-7 + -1x)(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 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 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 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

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, -7, 1.333333333}

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