2(3p+7)(p-2)=0

Solution for 2(3p+7)(p-2)=0 equation:

Simplifying
2(3p + 7)(p + -2) = 0

Reorder the terms:
2(7 + 3p)(p + -2) = 0

Reorder the terms:
2(7 + 3p)(-2 + p) = 0

Multiply (7 + 3p) * (-2 + p)
2(7(-2 + p) + 3p * (-2 + p)) = 0
2((-2 * 7 + p * 7) + 3p * (-2 + p)) = 0
2((-14 + 7p) + 3p * (-2 + p)) = 0
2(-14 + 7p + (-2 * 3p + p * 3p)) = 0
2(-14 + 7p + (-6p + 3p2)) = 0

Combine like terms: 7p + -6p = 1p
2(-14 + 1p + 3p2) = 0
(-14 * 2 + 1p * 2 + 3p2 * 2) = 0
(-28 + 2p + 6p2) = 0

Solving
-28 + 2p + 6p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + p + 3p2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -3p)' equal to zero and attempt to solve:

Simplifying
-7 + -3p = 0

Solving
-7 + -3p = 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 + -3p = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3p = 0 + 7
-3p = 0 + 7

Combine like terms: 0 + 7 = 7
-3p = 7

Divide each side by '-3'.
p = -2.333333333

Simplifying
p = -2.333333333
Subproblem 2
Set the factor '(2 + -1p)' equal to zero and attempt to solve:

Simplifying
2 + -1p = 0

Solving
2 + -1p = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1p = 0 + -2
-1p = 0 + -2

Combine like terms: 0 + -2 = -2
-1p = -2

Divide each side by '-1'.
p = 2

Simplifying
p = 2
Solution
p = {-2.333333333, 2}