4s^2=6+10s

Solution for 4s^2=6+10s equation:

Simplifying
4s2 = 6 + 10s

Solving
4s2 = 6 + 10s

Solving for variable 's'.

Reorder the terms:
-6 + -10s + 4s2 = 6 + 10s + -6 + -10s

Reorder the terms:
-6 + -10s + 4s2 = 6 + -6 + 10s + -10s

Combine like terms: 6 + -6 = 0
-6 + -10s + 4s2 = 0 + 10s + -10s
-6 + -10s + 4s2 = 10s + -10s

Combine like terms: 10s + -10s = 0
-6 + -10s + 4s2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -5s + 2s2) = 0

Factor a trinomial.
2((-1 + -2s)(3 + -1s)) = 0

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

Simplifying
-1 + -2s = 0

Solving
-1 + -2s = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2s = 0 + 1

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

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

Divide each side by '-2'.
s = -0.5

Simplifying
s = -0.5
Subproblem 2
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
Solution
s = {-0.5, 3}