2p(p-7)=6-3p

Solution for 2p(p-7)=6-3p equation:

Simplifying
2p(p + -7) = 6 + -3p

Reorder the terms:
2p(-7 + p) = 6 + -3p
(-7 * 2p + p * 2p) = 6 + -3p
(-14p + 2p2) = 6 + -3p

Solving
-14p + 2p2 = 6 + -3p

Solving for variable 'p'.

Reorder the terms:
-6 + -14p + 3p + 2p2 = 6 + -3p + -6 + 3p

Combine like terms: -14p + 3p = -11p
-6 + -11p + 2p2 = 6 + -3p + -6 + 3p

Reorder the terms:
-6 + -11p + 2p2 = 6 + -6 + -3p + 3p

Combine like terms: 6 + -6 = 0
-6 + -11p + 2p2 = 0 + -3p + 3p
-6 + -11p + 2p2 = -3p + 3p

Combine like terms: -3p + 3p = 0
-6 + -11p + 2p2 = 0

Factor a trinomial.
(-1 + -2p)(6 + -1p) = 0

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

Simplifying
-1 + -2p = 0

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

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

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

Divide each side by '-2'.
p = -0.5

Simplifying
p = -0.5
Subproblem 2
Set the factor '(6 + -1p)' equal to zero and attempt to solve:

Simplifying
6 + -1p = 0

Solving
6 + -1p = 0

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

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

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

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

Divide each side by '-1'.
p = 6

Simplifying
p = 6
Solution
p = {-0.5, 6}