3p(2p-1)-9=6(p+1)2

Solution for 3p(2p-1)-9=6(p+1)2 equation:

Simplifying
3p(2p + -1) + -9 = 6(p + 1) * 2

Reorder the terms:
3p(-1 + 2p) + -9 = 6(p + 1) * 2
(-1 * 3p + 2p * 3p) + -9 = 6(p + 1) * 2
(-3p + 6p2) + -9 = 6(p + 1) * 2

Reorder the terms:
-9 + -3p + 6p2 = 6(p + 1) * 2

Reorder the terms:
-9 + -3p + 6p2 = 6(1 + p) * 2

Reorder the terms for easier multiplication:
-9 + -3p + 6p2 = 6 * 2(1 + p)

Multiply 6 * 2
-9 + -3p + 6p2 = 12(1 + p)
-9 + -3p + 6p2 = (1 * 12 + p * 12)
-9 + -3p + 6p2 = (12 + 12p)

Solving
-9 + -3p + 6p2 = 12 + 12p

Solving for variable 'p'.

Reorder the terms:
-9 + -12 + -3p + -12p + 6p2 = 12 + 12p + -12 + -12p

Combine like terms: -9 + -12 = -21
-21 + -3p + -12p + 6p2 = 12 + 12p + -12 + -12p

Combine like terms: -3p + -12p = -15p
-21 + -15p + 6p2 = 12 + 12p + -12 + -12p

Reorder the terms:
-21 + -15p + 6p2 = 12 + -12 + 12p + -12p

Combine like terms: 12 + -12 = 0
-21 + -15p + 6p2 = 0 + 12p + -12p
-21 + -15p + 6p2 = 12p + -12p

Combine like terms: 12p + -12p = 0
-21 + -15p + 6p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + -5p + 2p2) = 0

Factor a trinomial.
3((-1 + -1p)(7 + -2p)) = 0

Ignore the factor 3.
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 '(7 + -2p)' equal to zero and attempt to solve:

Simplifying
7 + -2p = 0

Solving
7 + -2p = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2p = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2p = 0 + -7
-2p = 0 + -7

Combine like terms: 0 + -7 = -7
-2p = -7

Divide each side by '-2'.
p = 3.5

Simplifying
p = 3.5
Solution
p = {-1, 3.5}