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

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

Simplifying
4p2 + 2p = 3(p2 + -1p + 2)

Reorder the terms:
2p + 4p2 = 3(p2 + -1p + 2)

Reorder the terms:
2p + 4p2 = 3(2 + -1p + p2)
2p + 4p2 = (2 * 3 + -1p * 3 + p2 * 3)
2p + 4p2 = (6 + -3p + 3p2)

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

Solving for variable 'p'.

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

Combine like terms: 2p + 3p = 5p
-6 + 5p + 4p2 + -3p2 = 6 + -3p + 3p2 + -6 + 3p + -3p2

Combine like terms: 4p2 + -3p2 = 1p2
-6 + 5p + 1p2 = 6 + -3p + 3p2 + -6 + 3p + -3p2

Reorder the terms:
-6 + 5p + 1p2 = 6 + -6 + -3p + 3p + 3p2 + -3p2

Combine like terms: 6 + -6 = 0
-6 + 5p + 1p2 = 0 + -3p + 3p + 3p2 + -3p2
-6 + 5p + 1p2 = -3p + 3p + 3p2 + -3p2

Combine like terms: -3p + 3p = 0
-6 + 5p + 1p2 = 0 + 3p2 + -3p2
-6 + 5p + 1p2 = 3p2 + -3p2

Combine like terms: 3p2 + -3p2 = 0
-6 + 5p + 1p2 = 0

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

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

Simplifying
1 + -1p = 0

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

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

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

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

Simplifying
p = 1
Solution
p = {-6, 1}