4s(3s+8)(7-5s)=0

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Solution for 4s(3s+8)(7-5s)=0 equation: 


Simplifying
4s(3s + 8)(7 + -5s) = 0

Reorder the terms:
4s(8 + 3s)(7 + -5s) = 0

Multiply (8 + 3s) * (7 + -5s)
4s(8(7 + -5s) + 3s * (7 + -5s)) = 0
4s((7 * 8 + -5s * 8) + 3s * (7 + -5s)) = 0
4s((56 + -40s) + 3s * (7 + -5s)) = 0
4s(56 + -40s + (7 * 3s + -5s * 3s)) = 0
4s(56 + -40s + (21s + -15s2)) = 0

Combine like terms: -40s + 21s = -19s
4s(56 + -19s + -15s2) = 0
(56 * 4s + -19s * 4s + -15s2 * 4s) = 0
(224s + -76s2 + -60s3) = 0

Solving
224s + -76s2 + -60s3 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '4s'.
4s(56 + -19s + -15s2) = 0

Factor a trinomial.
4s((7 + -5s)(8 + 3s)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 's' equal to zero and attempt to solve:

Simplifying
s = 0

Solving
s = 0

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

Simplifying
s = 0

Subproblem 2
Set the factor '(7 + -5s)' equal to zero and attempt to solve:

Simplifying
7 + -5s = 0

Solving
7 + -5s = 0

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

Add '-7' to each side of the equation.
7 + -7 + -5s = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5s = 0 + -7
-5s = 0 + -7

Combine like terms: 0 + -7 = -7
-5s = -7

Divide each side by '-5'.
s = 1.4

Simplifying
s = 1.4

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

Simplifying
8 + 3s = 0

Solving
8 + 3s = 0

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

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

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

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

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

Simplifying
s = -2.666666667
Solution
s = {0, 1.4, -2.666666667}

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