3(x+5)(8x-3)=0

Solution for 3(x+5)(8x-3)=0 equation:

Simplifying
3(x + 5)(8x + -3) = 0

Reorder the terms:
3(5 + x)(8x + -3) = 0

Reorder the terms:
3(5 + x)(-3 + 8x) = 0

Multiply (5 + x) * (-3 + 8x)
3(5(-3 + 8x) + x(-3 + 8x)) = 0
3((-3 * 5 + 8x * 5) + x(-3 + 8x)) = 0
3((-15 + 40x) + x(-3 + 8x)) = 0
3(-15 + 40x + (-3 * x + 8x * x)) = 0
3(-15 + 40x + (-3x + 8x2)) = 0

Combine like terms: 40x + -3x = 37x
3(-15 + 37x + 8x2) = 0
(-15 * 3 + 37x * 3 + 8x2 * 3) = 0
(-45 + 111x + 24x2) = 0

Solving
-45 + 111x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + 37x + 8x2) = 0

Factor a trinomial.
3((-5 + -1x)(3 + -8x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(3 + -8x)' equal to zero and attempt to solve:

Simplifying
3 + -8x = 0

Solving
3 + -8x = 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 + -8x = 0 + -3

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

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

Divide each side by '-8'.
x = 0.375

Simplifying
x = 0.375
Solution
x = {-5, 0.375}