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

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


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

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

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

Multiply (-7 + 2x) * (8 + 3x)
x(-7(8 + 3x) + 2x * (8 + 3x)) = 0
x((8 * -7 + 3x * -7) + 2x * (8 + 3x)) = 0
x((-56 + -21x) + 2x * (8 + 3x)) = 0
x(-56 + -21x + (8 * 2x + 3x * 2x)) = 0
x(-56 + -21x + (16x + 6x2)) = 0

Combine like terms: -21x + 16x = -5x
x(-56 + -5x + 6x2) = 0
(-56 * x + -5x * x + 6x2 * x) = 0
(-56x + -5x2 + 6x3) = 0

Solving
-56x + -5x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-56 + -5x + 6x2) = 0

Factor a trinomial.
x((-8 + -3x)(7 + -2x)) = 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 '(-8 + -3x)' equal to zero and attempt to solve:

Simplifying
-8 + -3x = 0

Solving
-8 + -3x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3x = 0 + 8
-3x = 0 + 8

Combine like terms: 0 + 8 = 8
-3x = 8

Divide each side by '-3'.
x = -2.666666667

Simplifying
x = -2.666666667

Subproblem 3
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
Solution
x = {0, -2.666666667, 3.5}

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