4s^2+85=(3s+2)(3s+2)

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Solution for 4s^2+85=(3s+2)(3s+2) equation: 


Simplifying
4s2 + 85 = (3s + 2)(3s + 2)

Reorder the terms:
85 + 4s2 = (3s + 2)(3s + 2)

Reorder the terms:
85 + 4s2 = (2 + 3s)(3s + 2)

Reorder the terms:
85 + 4s2 = (2 + 3s)(2 + 3s)

Multiply (2 + 3s) * (2 + 3s)
85 + 4s2 = (2(2 + 3s) + 3s * (2 + 3s))
85 + 4s2 = ((2 * 2 + 3s * 2) + 3s * (2 + 3s))
85 + 4s2 = ((4 + 6s) + 3s * (2 + 3s))
85 + 4s2 = (4 + 6s + (2 * 3s + 3s * 3s))
85 + 4s2 = (4 + 6s + (6s + 9s2))

Combine like terms: 6s + 6s = 12s
85 + 4s2 = (4 + 12s + 9s2)

Solving
85 + 4s2 = 4 + 12s + 9s2

Solving for variable 's'.

Reorder the terms:
85 + -4 + -12s + 4s2 + -9s2 = 4 + 12s + 9s2 + -4 + -12s + -9s2

Combine like terms: 85 + -4 = 81
81 + -12s + 4s2 + -9s2 = 4 + 12s + 9s2 + -4 + -12s + -9s2

Combine like terms: 4s2 + -9s2 = -5s2
81 + -12s + -5s2 = 4 + 12s + 9s2 + -4 + -12s + -9s2

Reorder the terms:
81 + -12s + -5s2 = 4 + -4 + 12s + -12s + 9s2 + -9s2

Combine like terms: 4 + -4 = 0
81 + -12s + -5s2 = 0 + 12s + -12s + 9s2 + -9s2
81 + -12s + -5s2 = 12s + -12s + 9s2 + -9s2

Combine like terms: 12s + -12s = 0
81 + -12s + -5s2 = 0 + 9s2 + -9s2
81 + -12s + -5s2 = 9s2 + -9s2

Combine like terms: 9s2 + -9s2 = 0
81 + -12s + -5s2 = 0

Factor a trinomial.
(3 + -1s)(27 + 5s) = 0


Subproblem 1
Set the factor '(3 + -1s)' equal to zero and attempt to solve:

Simplifying
3 + -1s = 0

Solving
3 + -1s = 0

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

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

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

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

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

Simplifying
s = 3

Subproblem 2
Set the factor '(27 + 5s)' equal to zero and attempt to solve:

Simplifying
27 + 5s = 0

Solving
27 + 5s = 0

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

Add '-27' to each side of the equation.
27 + -27 + 5s = 0 + -27

Combine like terms: 27 + -27 = 0
0 + 5s = 0 + -27
5s = 0 + -27

Combine like terms: 0 + -27 = -27
5s = -27

Divide each side by '5'.
s = -5.4

Simplifying
s = -5.4
Solution
s = {3, -5.4}

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