4s^2-4s+52=3s^2+13s

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Solution for 4s^2-4s+52=3s^2+13s equation: 


Simplifying
4s2 + -4s + 52 = 3s2 + 13s

Reorder the terms:
52 + -4s + 4s2 = 3s2 + 13s

Reorder the terms:
52 + -4s + 4s2 = 13s + 3s2

Solving
52 + -4s + 4s2 = 13s + 3s2

Solving for variable 's'.

Reorder the terms:
52 + -4s + -13s + 4s2 + -3s2 = 13s + 3s2 + -13s + -3s2

Combine like terms: -4s + -13s = -17s
52 + -17s + 4s2 + -3s2 = 13s + 3s2 + -13s + -3s2

Combine like terms: 4s2 + -3s2 = 1s2
52 + -17s + 1s2 = 13s + 3s2 + -13s + -3s2

Reorder the terms:
52 + -17s + 1s2 = 13s + -13s + 3s2 + -3s2

Combine like terms: 13s + -13s = 0
52 + -17s + 1s2 = 0 + 3s2 + -3s2
52 + -17s + 1s2 = 3s2 + -3s2

Combine like terms: 3s2 + -3s2 = 0
52 + -17s + 1s2 = 0

Factor a trinomial.
(4 + -1s)(13 + -1s) = 0


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 '(13 + -1s)' equal to zero and attempt to solve:

Simplifying
13 + -1s = 0

Solving
13 + -1s = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1s = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1s = 0 + -13
-1s = 0 + -13

Combine like terms: 0 + -13 = -13
-1s = -13

Divide each side by '-1'.
s = 13

Simplifying
s = 13
Solution
s = {4, 13}

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