2s(8s+7)-4s=3(4s+1)-5

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Solution for 2s(8s+7)-4s=3(4s+1)-5 equation: 


Simplifying
2s(8s + 7) + -4s = 3(4s + 1) + -5

Reorder the terms:
2s(7 + 8s) + -4s = 3(4s + 1) + -5
(7 * 2s + 8s * 2s) + -4s = 3(4s + 1) + -5
(14s + 16s2) + -4s = 3(4s + 1) + -5

Reorder the terms:
14s + -4s + 16s2 = 3(4s + 1) + -5

Combine like terms: 14s + -4s = 10s
10s + 16s2 = 3(4s + 1) + -5

Reorder the terms:
10s + 16s2 = 3(1 + 4s) + -5
10s + 16s2 = (1 * 3 + 4s * 3) + -5
10s + 16s2 = (3 + 12s) + -5

Reorder the terms:
10s + 16s2 = 3 + -5 + 12s

Combine like terms: 3 + -5 = -2
10s + 16s2 = -2 + 12s

Solving
10s + 16s2 = -2 + 12s

Solving for variable 's'.

Reorder the terms:
2 + 10s + -12s + 16s2 = -2 + 12s + 2 + -12s

Combine like terms: 10s + -12s = -2s
2 + -2s + 16s2 = -2 + 12s + 2 + -12s

Reorder the terms:
2 + -2s + 16s2 = -2 + 2 + 12s + -12s

Combine like terms: -2 + 2 = 0
2 + -2s + 16s2 = 0 + 12s + -12s
2 + -2s + 16s2 = 12s + -12s

Combine like terms: 12s + -12s = 0
2 + -2s + 16s2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -1s + 8s2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -1s + 8s2)' equal to zero and attempt to solve:

Simplifying
1 + -1s + 8s2 = 0

Solving
1 + -1s + 8s2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
0.125 + -0.125s + s2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + -0.125s + -0.125 + s2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + -0.125s + s2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + -0.125s + s2 = 0 + -0.125
-0.125s + s2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
-0.125s + s2 = -0.125

The s term is -0.125s.  Take half its coefficient (-0.0625).
Square it (0.00390625) and add it to both sides.

Add '0.00390625' to each side of the equation.
-0.125s + 0.00390625 + s2 = -0.125 + 0.00390625

Reorder the terms:
0.00390625 + -0.125s + s2 = -0.125 + 0.00390625

Combine like terms: -0.125 + 0.00390625 = -0.12109375
0.00390625 + -0.125s + s2 = -0.12109375

Factor a perfect square on the left side:
(s + -0.0625)(s + -0.0625) = -0.12109375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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