6p^2+6p-8=0

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Solution for 6p^2+6p-8=0 equation: 


Simplifying
6p2 + 6p + -8 = 0

Reorder the terms:
-8 + 6p + 6p2 = 0

Solving
-8 + 6p + 6p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 3p + 3p2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + 3p + 3p2)' equal to zero and attempt to solve:

Simplifying
-4 + 3p + 3p2 = 0

Solving
-4 + 3p + 3p2 = 0

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

Divide each side by '3'.
-1.333333333 + p + p2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + p + 1.333333333 + p2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + p + p2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + p + p2 = 0 + 1.333333333
p + p2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
p + p2 = 1.333333333

The p term is p.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + p2 = 1.333333333 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + p2 = 1.333333333 + 0.25

Combine like terms: 1.333333333 + 0.25 = 1.583333333
1.25 + p2 = 1.583333333

Factor a perfect square on the left side:
(p + 0.5)(p + 0.5) = 1.583333333

Calculate the square root of the right side: 1.258305739

Break this problem into two subproblems by setting 
(p + 0.5) equal to 1.258305739 and -1.258305739.


Subproblem 1
p + 0.5 = 1.258305739

Simplifying
p + 0.5 = 1.258305739

Reorder the terms:
0.5 + p = 1.258305739

Solving
0.5 + p = 1.258305739

Solving for variable 'p'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + p = 1.258305739 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + p = 1.258305739 + -0.5
p = 1.258305739 + -0.5

Combine like terms: 1.258305739 + -0.5 = 0.758305739
p = 0.758305739

Simplifying
p = 0.758305739


Subproblem 2
p + 0.5 = -1.258305739

Simplifying
p + 0.5 = -1.258305739

Reorder the terms:
0.5 + p = -1.258305739

Solving
0.5 + p = -1.258305739

Solving for variable 'p'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + p = -1.258305739 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + p = -1.258305739 + -0.5
p = -1.258305739 + -0.5

Combine like terms: -1.258305739 + -0.5 = -1.758305739
p = -1.758305739

Simplifying
p = -1.758305739


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.758305739, -1.758305739}
Solution
p = {0.758305739, -1.758305739}

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