5p^2-6=2p^2-4p-6

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Solution for 5p^2-6=2p^2-4p-6 equation:


Simplifying
5p2 + -6 = 2p2 + -4p + -6

Reorder the terms:
-6 + 5p2 = 2p2 + -4p + -6

Reorder the terms:
-6 + 5p2 = -6 + -4p + 2p2

Add '6' to each side of the equation.
-6 + 6 + 5p2 = -6 + -4p + 6 + 2p2

Combine like terms: -6 + 6 = 0
0 + 5p2 = -6 + -4p + 6 + 2p2
5p2 = -6 + -4p + 6 + 2p2

Reorder the terms:
5p2 = -6 + 6 + -4p + 2p2

Combine like terms: -6 + 6 = 0
5p2 = 0 + -4p + 2p2
5p2 = -4p + 2p2

Solving
5p2 = -4p + 2p2

Solving for variable 'p'.

Reorder the terms:
4p + 5p2 + -2p2 = -4p + 2p2 + 4p + -2p2

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'p'.
p(4 + 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 '(4 + 3p)' equal to zero and attempt to solve: Simplifying 4 + 3p = 0 Solving 4 + 3p = 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 + 3p = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3p = 0 + -4 3p = 0 + -4 Combine like terms: 0 + -4 = -4 3p = -4 Divide each side by '3'. p = -1.333333333 Simplifying p = -1.333333333

Solution

p = {0, -1.333333333}

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