p-(p+1)=6p(p-2)+5p

Solution for p-(p+1)=6p(p-2)+5p equation:

Simplifying
p + -1(p + 1) = 6p(p + -2) + 5p

Reorder the terms:
p + -1(1 + p) = 6p(p + -2) + 5p
p + (1 * -1 + p * -1) = 6p(p + -2) + 5p
p + (-1 + -1p) = 6p(p + -2) + 5p

Reorder the terms:
-1 + p + -1p = 6p(p + -2) + 5p

Combine like terms: p + -1p = 0
-1 + 0 = 6p(p + -2) + 5p
-1 = 6p(p + -2) + 5p

Reorder the terms:
-1 = 6p(-2 + p) + 5p
-1 = (-2 * 6p + p * 6p) + 5p
-1 = (-12p + 6p2) + 5p

Reorder the terms:
-1 = -12p + 5p + 6p2

Combine like terms: -12p + 5p = -7p
-1 = -7p + 6p2

Solving
-1 = -7p + 6p2

Solving for variable 'p'.

Reorder the terms:
-1 + 7p + -6p2 = -7p + 7p + 6p2 + -6p2

Combine like terms: -7p + 7p = 0
-1 + 7p + -6p2 = 0 + 6p2 + -6p2
-1 + 7p + -6p2 = 6p2 + -6p2

Combine like terms: 6p2 + -6p2 = 0
-1 + 7p + -6p2 = 0

Factor a trinomial.
(-1 + p)(1 + -6p) = 0

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

Simplifying
-1 + p = 0

Solving
-1 + p = 0

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

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

Combine like terms: -1 + 1 = 0
0 + p = 0 + 1
p = 0 + 1

Combine like terms: 0 + 1 = 1
p = 1

Simplifying
p = 1
Subproblem 2
Set the factor '(1 + -6p)' equal to zero and attempt to solve:

Simplifying
1 + -6p = 0

Solving
1 + -6p = 0

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

Add '-1' to each side of the equation.
1 + -1 + -6p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6p = 0 + -1
-6p = 0 + -1

Combine like terms: 0 + -1 = -1
-6p = -1

Divide each side by '-6'.
p = 0.1666666667

Simplifying
p = 0.1666666667
Solution
p = {1, 0.1666666667}