24(p^2-1)=55p

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Solution for 24(p^2-1)=55p equation:


Simplifying
24(p2 + -1) = 55p

Reorder the terms:
24(-1 + p2) = 55p
(-1 * 24 + p2 * 24) = 55p
(-24 + 24p2) = 55p

Solving
-24 + 24p2 = 55p

Solving for variable 'p'.

Reorder the terms:
-24 + -55p + 24p2 = 55p + -55p

Combine like terms: 55p + -55p = 0
-24 + -55p + 24p2 = 0

Factor a trinomial.
(-3 + -8p)(8 + -3p) = 0

Subproblem 1

Set the factor '(-3 + -8p)' equal to zero and attempt to solve: Simplifying -3 + -8p = 0 Solving -3 + -8p = 0 Move all terms containing p to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -8p = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8p = 0 + 3 -8p = 0 + 3 Combine like terms: 0 + 3 = 3 -8p = 3 Divide each side by '-8'. p = -0.375 Simplifying p = -0.375

Subproblem 2

Set the factor '(8 + -3p)' equal to zero and attempt to solve: Simplifying 8 + -3p = 0 Solving 8 + -3p = 0 Move all terms containing p to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3p = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3p = 0 + -8 -3p = 0 + -8 Combine like terms: 0 + -8 = -8 -3p = -8 Divide each side by '-3'. p = 2.666666667 Simplifying p = 2.666666667

Solution

p = {-0.375, 2.666666667}

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