(3p-2)(p+9)=0

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Solution for (3p-2)(p+9)=0 equation:


Simplifying
(3p + -2)(p + 9) = 0

Reorder the terms:
(-2 + 3p)(p + 9) = 0

Reorder the terms:
(-2 + 3p)(9 + p) = 0

Multiply (-2 + 3p) * (9 + p)
(-2(9 + p) + 3p * (9 + p)) = 0
((9 * -2 + p * -2) + 3p * (9 + p)) = 0
((-18 + -2p) + 3p * (9 + p)) = 0
(-18 + -2p + (9 * 3p + p * 3p)) = 0
(-18 + -2p + (27p + 3p2)) = 0

Combine like terms: -2p + 27p = 25p
(-18 + 25p + 3p2) = 0

Solving
-18 + 25p + 3p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-9 + -1p)(2 + -3p) = 0

Subproblem 1

Set the factor '(-9 + -1p)' equal to zero and attempt to solve: Simplifying -9 + -1p = 0 Solving -9 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1p = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1p = 0 + 9 -1p = 0 + 9 Combine like terms: 0 + 9 = 9 -1p = 9 Divide each side by '-1'. p = -9 Simplifying p = -9

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 = {-9, 0.6666666667}

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