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

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


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

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

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

Multiply (3 + x) * (-7 + 8x)
x(3(-7 + 8x) + x(-7 + 8x)) = 0
x((-7 * 3 + 8x * 3) + x(-7 + 8x)) = 0
x((-21 + 24x) + x(-7 + 8x)) = 0
x(-21 + 24x + (-7 * x + 8x * x)) = 0
x(-21 + 24x + (-7x + 8x2)) = 0

Combine like terms: 24x + -7x = 17x
x(-21 + 17x + 8x2) = 0
(-21 * x + 17x * x + 8x2 * x) = 0
(-21x + 17x2 + 8x3) = 0

Solving
-21x + 17x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-21 + 17x + 8x2) = 0

Factor a trinomial.
x((-3 + -1x)(7 + -8x)) = 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 '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 3
Set the factor '(7 + -8x)' equal to zero and attempt to solve:

Simplifying
7 + -8x = 0

Solving
7 + -8x = 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 + -8x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -8x = 0 + -7
-8x = 0 + -7

Combine like terms: 0 + -7 = -7
-8x = -7

Divide each side by '-8'.
x = 0.875

Simplifying
x = 0.875
Solution
x = {0, -3, 0.875}

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