5p(p-2)=4-2p

Solution for 5p(p-2)=4-2p equation:

Simplifying
5p(p + -2) = 4 + -2p

Reorder the terms:
5p(-2 + p) = 4 + -2p
(-2 * 5p + p * 5p) = 4 + -2p
(-10p + 5p2) = 4 + -2p

Solving
-10p + 5p2 = 4 + -2p

Solving for variable 'p'.

Reorder the terms:
-4 + -10p + 2p + 5p2 = 4 + -2p + -4 + 2p

Combine like terms: -10p + 2p = -8p
-4 + -8p + 5p2 = 4 + -2p + -4 + 2p

Reorder the terms:
-4 + -8p + 5p2 = 4 + -4 + -2p + 2p

Combine like terms: 4 + -4 = 0
-4 + -8p + 5p2 = 0 + -2p + 2p
-4 + -8p + 5p2 = -2p + 2p

Combine like terms: -2p + 2p = 0
-4 + -8p + 5p2 = 0

Factor a trinomial.
(-2 + -5p)(2 + -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 '(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 = {-0.4, 2}