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

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


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

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

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

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

Combine like terms: 16x + -7x = 9x
3x(-56 + 9x + 2x2) = 0
(-56 * 3x + 9x * 3x + 2x2 * 3x) = 0
(-168x + 27x2 + 6x3) = 0

Solving
-168x + 27x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-56 + 9x + 2x2) = 0

Factor a trinomial.
3x((-8 + -1x)(7 + -2x)) = 0

Ignore the factor 3.

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

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 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 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

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, -8, 3.5}

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