p^2=2p-2p^2

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Solution for p^2=2p-2p^2 equation:


Simplifying
p2 = 2p + -2p2

Solving
p2 = 2p + -2p2

Solving for variable 'p'.

Reorder the terms:
-2p + p2 + 2p2 = 2p + -2p2 + -2p + 2p2

Combine like terms: p2 + 2p2 = 3p2
-2p + 3p2 = 2p + -2p2 + -2p + 2p2

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

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

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

Factor out the Greatest Common Factor (GCF), 'p'.
p(-2 + 3p) = 0

Subproblem 1

Set the factor 'p' equal to zero and attempt to solve: Simplifying p = 0 Solving p = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p = 0

Subproblem 2

Set the factor '(-2 + 3p)' equal to zero and attempt to solve: Simplifying -2 + 3p = 0 Solving -2 + 3p = 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 + 3p = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3p = 0 + 2 3p = 0 + 2 Combine like terms: 0 + 2 = 2 3p = 2 Divide each side by '3'. p = 0.6666666667 Simplifying p = 0.6666666667

Solution

p = {0, 0.6666666667}

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