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

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

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

Reorder the terms:
2p(-3 + p) = 3p + -4
(-3 * 2p + p * 2p) = 3p + -4
(-6p + 2p2) = 3p + -4

Reorder the terms:
-6p + 2p2 = -4 + 3p

Solving
-6p + 2p2 = -4 + 3p

Solving for variable 'p'.

Reorder the terms:
4 + -6p + -3p + 2p2 = -4 + 3p + 4 + -3p

Combine like terms: -6p + -3p = -9p
4 + -9p + 2p2 = -4 + 3p + 4 + -3p

Reorder the terms:
4 + -9p + 2p2 = -4 + 4 + 3p + -3p

Combine like terms: -4 + 4 = 0
4 + -9p + 2p2 = 0 + 3p + -3p
4 + -9p + 2p2 = 3p + -3p

Combine like terms: 3p + -3p = 0
4 + -9p + 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}