(p-3)(2p+1)+6=0

Solution for (p-3)(2p+1)+6=0 equation:

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

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

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

Multiply (-3 + p) * (1 + 2p)
(-3(1 + 2p) + p(1 + 2p)) + 6 = 0
((1 * -3 + 2p * -3) + p(1 + 2p)) + 6 = 0
((-3 + -6p) + p(1 + 2p)) + 6 = 0
(-3 + -6p + (1 * p + 2p * p)) + 6 = 0
(-3 + -6p + (1p + 2p2)) + 6 = 0

Combine like terms: -6p + 1p = -5p
(-3 + -5p + 2p2) + 6 = 0

Reorder the terms:
-3 + 6 + -5p + 2p2 = 0

Combine like terms: -3 + 6 = 3
3 + -5p + 2p2 = 0

Solving
3 + -5p + 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}