p-(p+30)=6p(p-5)+4p

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Solution for p-(p+30)=6p(p-5)+4p equation: 


Simplifying
p + -1(p + 30) = 6p(p + -5) + 4p

Reorder the terms:
p + -1(30 + p) = 6p(p + -5) + 4p
p + (30 * -1 + p * -1) = 6p(p + -5) + 4p
p + (-30 + -1p) = 6p(p + -5) + 4p

Reorder the terms:
-30 + p + -1p = 6p(p + -5) + 4p

Combine like terms: p + -1p = 0
-30 + 0 = 6p(p + -5) + 4p
-30 = 6p(p + -5) + 4p

Reorder the terms:
-30 = 6p(-5 + p) + 4p
-30 = (-5 * 6p + p * 6p) + 4p
-30 = (-30p + 6p2) + 4p

Reorder the terms:
-30 = -30p + 4p + 6p2

Combine like terms: -30p + 4p = -26p
-30 = -26p + 6p2

Solving
-30 = -26p + 6p2

Solving for variable 'p'.

Reorder the terms:
-30 + 26p + -6p2 = -26p + 26p + 6p2 + -6p2

Combine like terms: -26p + 26p = 0
-30 + 26p + -6p2 = 0 + 6p2 + -6p2
-30 + 26p + -6p2 = 6p2 + -6p2

Combine like terms: 6p2 + -6p2 = 0
-30 + 26p + -6p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 13p + -3p2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-15 + 13p + -3p2)' equal to zero and attempt to solve:

Simplifying
-15 + 13p + -3p2 = 0

Solving
-15 + 13p + -3p2 = 0

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

Divide each side by '-3'.
5 + -4.333333333p + p2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -4.333333333p + -5 + p2 = 0 + -5

Reorder the terms:
5 + -5 + -4.333333333p + p2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4.333333333p + p2 = 0 + -5
-4.333333333p + p2 = 0 + -5

Combine like terms: 0 + -5 = -5
-4.333333333p + p2 = -5

The p term is -4.333333333p.  Take half its coefficient (-2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
-4.333333333p + 4.694444446 + p2 = -5 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333p + p2 = -5 + 4.694444446

Combine like terms: -5 + 4.694444446 = -0.305555554
4.694444446 + -4.333333333p + p2 = -0.305555554

Factor a perfect square on the left side:
(p + -2.166666667)(p + -2.166666667) = -0.305555554

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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