2p(p-5)=4-3p

Solution for 2p(p-5)=4-3p equation:

Simplifying
2p(p + -5) = 4 + -3p

Reorder the terms:
2p(-5 + p) = 4 + -3p
(-5 * 2p + p * 2p) = 4 + -3p
(-10p + 2p2) = 4 + -3p

Solving
-10p + 2p2 = 4 + -3p

Solving for variable 'p'.

Reorder the terms:
-4 + -10p + 3p + 2p2 = 4 + -3p + -4 + 3p

Combine like terms: -10p + 3p = -7p
-4 + -7p + 2p2 = 4 + -3p + -4 + 3p

Reorder the terms:
-4 + -7p + 2p2 = 4 + -4 + -3p + 3p

Combine like terms: 4 + -4 = 0
-4 + -7p + 2p2 = 0 + -3p + 3p
-4 + -7p + 2p2 = -3p + 3p

Combine like terms: -3p + 3p = 0
-4 + -7p + 2p2 = 0

Factor a trinomial.
(-1 + -2p)(4 + -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 '(4 + -1p)' equal to zero and attempt to solve:

Simplifying
4 + -1p = 0

Solving
4 + -1p = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1p = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1p = 0 + -4
-1p = 0 + -4

Combine like terms: 0 + -4 = -4
-1p = -4

Divide each side by '-1'.
p = 4

Simplifying
p = 4
Solution
p = {-0.5, 4}