12p^2+18p-8=0

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Solution for 12p^2+18p-8=0 equation: 


Simplifying
12p2 + 18p + -8 = 0

Reorder the terms:
-8 + 18p + 12p2 = 0

Solving
-8 + 18p + 12p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 9p + 6p2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + 9p + 6p2)' equal to zero and attempt to solve:

Simplifying
-4 + 9p + 6p2 = 0

Solving
-4 + 9p + 6p2 = 0

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

Divide each side by '6'.
-0.6666666667 + 1.5p + p2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 1.5p + 0.6666666667 + p2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 1.5p + p2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 1.5p + p2 = 0 + 0.6666666667
1.5p + p2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
1.5p + p2 = 0.6666666667

The p term is 1.5p.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5p + 0.5625 + p2 = 0.6666666667 + 0.5625

Reorder the terms:
0.5625 + 1.5p + p2 = 0.6666666667 + 0.5625

Combine like terms: 0.6666666667 + 0.5625 = 1.2291666667
0.5625 + 1.5p + p2 = 1.2291666667

Factor a perfect square on the left side:
(p + 0.75)(p + 0.75) = 1.2291666667

Calculate the square root of the right side: 1.108677891

Break this problem into two subproblems by setting 
(p + 0.75) equal to 1.108677891 and -1.108677891.


Subproblem 1
p + 0.75 = 1.108677891

Simplifying
p + 0.75 = 1.108677891

Reorder the terms:
0.75 + p = 1.108677891

Solving
0.75 + p = 1.108677891

Solving for variable 'p'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + p = 1.108677891 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + p = 1.108677891 + -0.75
p = 1.108677891 + -0.75

Combine like terms: 1.108677891 + -0.75 = 0.358677891
p = 0.358677891

Simplifying
p = 0.358677891


Subproblem 2
p + 0.75 = -1.108677891

Simplifying
p + 0.75 = -1.108677891

Reorder the terms:
0.75 + p = -1.108677891

Solving
0.75 + p = -1.108677891

Solving for variable 'p'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + p = -1.108677891 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + p = -1.108677891 + -0.75
p = -1.108677891 + -0.75

Combine like terms: -1.108677891 + -0.75 = -1.858677891
p = -1.858677891

Simplifying
p = -1.858677891


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.358677891, -1.858677891}
Solution
p = {0.358677891, -1.858677891}

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