(p+5p-9)-(3p-6)+p(2p-4)=

Solution for (p+5p-9)-(3p-6)+p(2p-4)= equation:

Simplifying
(p + 5p + -9) + -1(3p + -6) + p(2p + -4) = 0

Reorder the terms:
(-9 + p + 5p) + -1(3p + -6) + p(2p + -4) = 0

Combine like terms: p + 5p = 6p
(-9 + 6p) + -1(3p + -6) + p(2p + -4) = 0

Remove parenthesis around (-9 + 6p)
-9 + 6p + -1(3p + -6) + p(2p + -4) = 0

Reorder the terms:
-9 + 6p + -1(-6 + 3p) + p(2p + -4) = 0
-9 + 6p + (-6 * -1 + 3p * -1) + p(2p + -4) = 0
-9 + 6p + (6 + -3p) + p(2p + -4) = 0

Reorder the terms:
-9 + 6p + 6 + -3p + p(-4 + 2p) = 0
-9 + 6p + 6 + -3p + (-4 * p + 2p * p) = 0
-9 + 6p + 6 + -3p + (-4p + 2p2) = 0

Reorder the terms:
-9 + 6 + 6p + -3p + -4p + 2p2 = 0

Combine like terms: -9 + 6 = -3
-3 + 6p + -3p + -4p + 2p2 = 0

Combine like terms: 6p + -3p = 3p
-3 + 3p + -4p + 2p2 = 0

Combine like terms: 3p + -4p = -1p
-3 + -1p + 2p2 = 0

Solving
-3 + -1p + 2p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-1 + -1p)(3 + -2p) = 0

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

Simplifying
-1 + -1p = 0

Solving
-1 + -1p = 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 + -1p = 0 + 1

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

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

Divide each side by '-1'.
p = -1

Simplifying
p = -1
Subproblem 2
Set the factor '(3 + -2p)' equal to zero and attempt to solve:

Simplifying
3 + -2p = 0

Solving
3 + -2p = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2p = 0 + -3
-2p = 0 + -3

Combine like terms: 0 + -3 = -3
-2p = -3

Divide each side by '-2'.
p = 1.5

Simplifying
p = 1.5
Solution
p = {-1, 1.5}