5p(p-3)=6-2p

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

Simplifying
5p(p + -3) = 6 + -2p

Reorder the terms:
5p(-3 + p) = 6 + -2p
(-3 * 5p + p * 5p) = 6 + -2p
(-15p + 5p2) = 6 + -2p

Solving
-15p + 5p2 = 6 + -2p

Solving for variable 'p'.

Reorder the terms:
-6 + -15p + 2p + 5p2 = 6 + -2p + -6 + 2p

Combine like terms: -15p + 2p = -13p
-6 + -13p + 5p2 = 6 + -2p + -6 + 2p

Reorder the terms:
-6 + -13p + 5p2 = 6 + -6 + -2p + 2p

Combine like terms: 6 + -6 = 0
-6 + -13p + 5p2 = 0 + -2p + 2p
-6 + -13p + 5p2 = -2p + 2p

Combine like terms: -2p + 2p = 0
-6 + -13p + 5p2 = 0

Factor a trinomial.
(-2 + -5p)(3 + -1p) = 0

Subproblem 1
Set the factor '(-2 + -5p)' equal to zero and attempt to solve:

Simplifying
-2 + -5p = 0

Solving
-2 + -5p = 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 + -5p = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5p = 0 + 2
-5p = 0 + 2

Combine like terms: 0 + 2 = 2
-5p = 2

Divide each side by '-5'.
p = -0.4

Simplifying
p = -0.4
Subproblem 2
Set the factor '(3 + -1p)' equal to zero and attempt to solve:

Simplifying
3 + -1p = 0

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

Combine like terms: 3 + -3 = 0
0 + -1p = 0 + -3
-1p = 0 + -3

Combine like terms: 0 + -3 = -3
-1p = -3

Divide each side by '-1'.
p = 3

Simplifying
p = 3
Solution
p = {-0.4, 3}