(7P+12)(18+2P)=0

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Solution for (7P+12)(18+2P)=0 equation: 


Simplifying
(7P + 12)(18 + 2P) = 0

Reorder the terms:
(12 + 7P)(18 + 2P) = 0

Multiply (12 + 7P) * (18 + 2P)
(12(18 + 2P) + 7P * (18 + 2P)) = 0
((18 * 12 + 2P * 12) + 7P * (18 + 2P)) = 0
((216 + 24P) + 7P * (18 + 2P)) = 0
(216 + 24P + (18 * 7P + 2P * 7P)) = 0
(216 + 24P + (126P + 14P2)) = 0

Combine like terms: 24P + 126P = 150P
(216 + 150P + 14P2) = 0

Solving
216 + 150P + 14P2 = 0

Solving for variable 'P'.

Factor out the Greatest Common Factor (GCF), '2'.
2(108 + 75P + 7P2) = 0

Factor a trinomial.
2((9 + P)(12 + 7P)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(9 + P)' equal to zero and attempt to solve:

Simplifying
9 + P = 0

Solving
9 + P = 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 + P = 0 + -9

Combine like terms: 9 + -9 = 0
0 + P = 0 + -9
P = 0 + -9

Combine like terms: 0 + -9 = -9
P = -9

Simplifying
P = -9

Subproblem 2
Set the factor '(12 + 7P)' equal to zero and attempt to solve:

Simplifying
12 + 7P = 0

Solving
12 + 7P = 0

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

Add '-12' to each side of the equation.
12 + -12 + 7P = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 7P = 0 + -12
7P = 0 + -12

Combine like terms: 0 + -12 = -12
7P = -12

Divide each side by '7'.
P = -1.714285714

Simplifying
P = -1.714285714
Solution
P = {-9, -1.714285714}

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