(-9p)(-10+3p)+7p(-9+3p)=

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Solution for (-9p)(-10+3p)+7p(-9+3p)= equation: 


Simplifying
(-9p)(-10 + 3p) + 7p(-9 + 3p) = 0

Remove parenthesis around (-9p)
-9p(-10 + 3p) + 7p(-9 + 3p) = 0
(-10 * -9p + 3p * -9p) + 7p(-9 + 3p) = 0
(90p + -27p2) + 7p(-9 + 3p) = 0
90p + -27p2 + (-9 * 7p + 3p * 7p) = 0
90p + -27p2 + (-63p + 21p2) = 0

Reorder the terms:
90p + -63p + -27p2 + 21p2 = 0

Combine like terms: 90p + -63p = 27p
27p + -27p2 + 21p2 = 0

Combine like terms: -27p2 + 21p2 = -6p2
27p + -6p2 = 0

Solving
27p + -6p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '3p'.
3p(9 + -2p) = 0

Ignore the factor 3.

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 '(9 + -2p)' equal to zero and attempt to solve:

Simplifying
9 + -2p = 0

Solving
9 + -2p = 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 + -2p = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2p = 0 + -9
-2p = 0 + -9

Combine like terms: 0 + -9 = -9
-2p = -9

Divide each side by '-2'.
p = 4.5

Simplifying
p = 4.5
Solution
p = {0, 4.5}

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