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

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


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

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

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

Multiply (4 + s) * (-7 + s)
5(4(-7 + s) + s(-7 + s)) = 0
5((-7 * 4 + s * 4) + s(-7 + s)) = 0
5((-28 + 4s) + s(-7 + s)) = 0
5(-28 + 4s + (-7 * s + s * s)) = 0
5(-28 + 4s + (-7s + s2)) = 0

Combine like terms: 4s + -7s = -3s
5(-28 + -3s + s2) = 0
(-28 * 5 + -3s * 5 + s2 * 5) = 0
(-140 + -15s + 5s2) = 0

Solving
-140 + -15s + 5s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-28 + -3s + s2) = 0

Factor a trinomial.
5((-4 + -1s)(7 + -1s)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-4 + -1s)' equal to zero and attempt to solve:

Simplifying
-4 + -1s = 0

Solving
-4 + -1s = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1s = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1s = 0 + 4
-1s = 0 + 4

Combine like terms: 0 + 4 = 4
-1s = 4

Divide each side by '-1'.
s = -4

Simplifying
s = -4

Subproblem 2
Set the factor '(7 + -1s)' equal to zero and attempt to solve:

Simplifying
7 + -1s = 0

Solving
7 + -1s = 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 + -1s = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1s = 0 + -7
-1s = 0 + -7

Combine like terms: 0 + -7 = -7
-1s = -7

Divide each side by '-1'.
s = 7

Simplifying
s = 7
Solution
s = {-4, 7}

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