p(4)+(1-p)(-2)=p(-3)+(1-p)(0)

Solution for p(4)+(1-p)(-2)=p(-3)+(1-p)(0) equation:

Simplifying
p(4) + (1 + -1p)(-2) = p(-3) + (1 + -1p)(0)

Reorder the terms for easier multiplication:
4p + (1 + -1p)(-2) = p(-3) + (1 + -1p)(0)

Reorder the terms for easier multiplication:
4p + -2(1 + -1p) = p(-3) + (1 + -1p)(0)
4p + (1 * -2 + -1p * -2) = p(-3) + (1 + -1p)(0)
4p + (-2 + 2p) = p(-3) + (1 + -1p)(0)

Reorder the terms:
-2 + 4p + 2p = p(-3) + (1 + -1p)(0)

Combine like terms: 4p + 2p = 6p
-2 + 6p = p(-3) + (1 + -1p)(0)

Reorder the terms for easier multiplication:
-2 + 6p = -3p + (1 + -1p)(0)

Reorder the terms for easier multiplication:
-2 + 6p = -3p + 0(1 + -1p)

Anything times zero is zero.
-2 + 6p = -3p + 0(1 + -1p)

Reorder the terms:
-2 + 6p = 0 + -3p
Remove the zero:
-2 + 6p = -3p

Solving
-2 + 6p = -3p

Solving for variable 'p'.

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

Add '3p' to each side of the equation.
-2 + 6p + 3p = -3p + 3p

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

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

Add '2' to each side of the equation.
-2 + 2 + 9p = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 9p = 0 + 2
9p = 0 + 2

Combine like terms: 0 + 2 = 2
9p = 2

Divide each side by '9'.
p = 0.2222222222

Simplifying
p = 0.2222222222