s^2+5s-4=(2s+1)(s-4)

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Solution for s^2+5s-4=(2s+1)(s-4) equation: 


Simplifying
s2 + 5s + -4 = (2s + 1)(s + -4)

Reorder the terms:
-4 + 5s + s2 = (2s + 1)(s + -4)

Reorder the terms:
-4 + 5s + s2 = (1 + 2s)(s + -4)

Reorder the terms:
-4 + 5s + s2 = (1 + 2s)(-4 + s)

Multiply (1 + 2s) * (-4 + s)
-4 + 5s + s2 = (1(-4 + s) + 2s * (-4 + s))
-4 + 5s + s2 = ((-4 * 1 + s * 1) + 2s * (-4 + s))
-4 + 5s + s2 = ((-4 + 1s) + 2s * (-4 + s))
-4 + 5s + s2 = (-4 + 1s + (-4 * 2s + s * 2s))
-4 + 5s + s2 = (-4 + 1s + (-8s + 2s2))

Combine like terms: 1s + -8s = -7s
-4 + 5s + s2 = (-4 + -7s + 2s2)

Add '4' to each side of the equation.
-4 + 5s + 4 + s2 = -4 + -7s + 4 + 2s2

Reorder the terms:
-4 + 4 + 5s + s2 = -4 + -7s + 4 + 2s2

Combine like terms: -4 + 4 = 0
0 + 5s + s2 = -4 + -7s + 4 + 2s2
5s + s2 = -4 + -7s + 4 + 2s2

Reorder the terms:
5s + s2 = -4 + 4 + -7s + 2s2

Combine like terms: -4 + 4 = 0
5s + s2 = 0 + -7s + 2s2
5s + s2 = -7s + 2s2

Solving
5s + s2 = -7s + 2s2

Solving for variable 's'.

Reorder the terms:
5s + 7s + s2 + -2s2 = -7s + 2s2 + 7s + -2s2

Combine like terms: 5s + 7s = 12s
12s + s2 + -2s2 = -7s + 2s2 + 7s + -2s2

Combine like terms: s2 + -2s2 = -1s2
12s + -1s2 = -7s + 2s2 + 7s + -2s2

Reorder the terms:
12s + -1s2 = -7s + 7s + 2s2 + -2s2

Combine like terms: -7s + 7s = 0
12s + -1s2 = 0 + 2s2 + -2s2
12s + -1s2 = 2s2 + -2s2

Combine like terms: 2s2 + -2s2 = 0
12s + -1s2 = 0

Factor out the Greatest Common Factor (GCF), 's'.
s(12 + -1s) = 0


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 '(12 + -1s)' equal to zero and attempt to solve:

Simplifying
12 + -1s = 0

Solving
12 + -1s = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1s = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1s = 0 + -12
-1s = 0 + -12

Combine like terms: 0 + -12 = -12
-1s = -12

Divide each side by '-1'.
s = 12

Simplifying
s = 12
Solution
s = {0, 12}

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