x(2x+8)(3x-7)=0

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Solution for x(2x+8)(3x-7)=0 equation: 


Simplifying
x(2x + 8)(3x + -7) = 0

Reorder the terms:
x(8 + 2x)(3x + -7) = 0

Reorder the terms:
x(8 + 2x)(-7 + 3x) = 0

Multiply (8 + 2x) * (-7 + 3x)
x(8(-7 + 3x) + 2x * (-7 + 3x)) = 0
x((-7 * 8 + 3x * 8) + 2x * (-7 + 3x)) = 0
x((-56 + 24x) + 2x * (-7 + 3x)) = 0
x(-56 + 24x + (-7 * 2x + 3x * 2x)) = 0
x(-56 + 24x + (-14x + 6x2)) = 0

Combine like terms: 24x + -14x = 10x
x(-56 + 10x + 6x2) = 0
(-56 * x + 10x * x + 6x2 * x) = 0
(-56x + 10x2 + 6x3) = 0

Solving
-56x + 10x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-28 + 5x + 3x2) = 0

Factor a trinomial.
2x((-4 + -1x)(7 + -3x)) = 0

Ignore the factor 2.

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 '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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, -4, 2.333333333}

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