9(3p-2)=3(p+4)(4-p)

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Solution for 9(3p-2)=3(p+4)(4-p) equation: 


Simplifying
9(3p + -2) = 3(p + 4)(4 + -1p)

Reorder the terms:
9(-2 + 3p) = 3(p + 4)(4 + -1p)
(-2 * 9 + 3p * 9) = 3(p + 4)(4 + -1p)
(-18 + 27p) = 3(p + 4)(4 + -1p)

Reorder the terms:
-18 + 27p = 3(4 + p)(4 + -1p)

Multiply (4 + p) * (4 + -1p)
-18 + 27p = 3(4(4 + -1p) + p(4 + -1p))
-18 + 27p = 3((4 * 4 + -1p * 4) + p(4 + -1p))
-18 + 27p = 3((16 + -4p) + p(4 + -1p))
-18 + 27p = 3(16 + -4p + (4 * p + -1p * p))
-18 + 27p = 3(16 + -4p + (4p + -1p2))

Combine like terms: -4p + 4p = 0
-18 + 27p = 3(16 + 0 + -1p2)
-18 + 27p = 3(16 + -1p2)
-18 + 27p = (16 * 3 + -1p2 * 3)
-18 + 27p = (48 + -3p2)

Solving
-18 + 27p = 48 + -3p2

Solving for variable 'p'.

Reorder the terms:
-18 + -48 + 27p + 3p2 = 48 + -3p2 + -48 + 3p2

Combine like terms: -18 + -48 = -66
-66 + 27p + 3p2 = 48 + -3p2 + -48 + 3p2

Reorder the terms:
-66 + 27p + 3p2 = 48 + -48 + -3p2 + 3p2

Combine like terms: 48 + -48 = 0
-66 + 27p + 3p2 = 0 + -3p2 + 3p2
-66 + 27p + 3p2 = -3p2 + 3p2

Combine like terms: -3p2 + 3p2 = 0
-66 + 27p + 3p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-22 + 9p + p2) = 0

Factor a trinomial.
3((-11 + -1p)(2 + -1p)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-11 + -1p)' equal to zero and attempt to solve:

Simplifying
-11 + -1p = 0

Solving
-11 + -1p = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1p = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1p = 0 + 11
-1p = 0 + 11

Combine like terms: 0 + 11 = 11
-1p = 11

Divide each side by '-1'.
p = -11

Simplifying
p = -11

Subproblem 2
Set the factor '(2 + -1p)' equal to zero and attempt to solve:

Simplifying
2 + -1p = 0

Solving
2 + -1p = 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 + -1p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1p = 0 + -2
-1p = 0 + -2

Combine like terms: 0 + -2 = -2
-1p = -2

Divide each side by '-1'.
p = 2

Simplifying
p = 2
Solution
p = {-11, 2}

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