18p^2-55=30p-7

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Solution for 18p^2-55=30p-7 equation: 


Simplifying
18p2 + -55 = 30p + -7

Reorder the terms:
-55 + 18p2 = 30p + -7

Reorder the terms:
-55 + 18p2 = -7 + 30p

Solving
-55 + 18p2 = -7 + 30p

Solving for variable 'p'.

Reorder the terms:
-55 + 7 + -30p + 18p2 = -7 + 30p + 7 + -30p

Combine like terms: -55 + 7 = -48
-48 + -30p + 18p2 = -7 + 30p + 7 + -30p

Reorder the terms:
-48 + -30p + 18p2 = -7 + 7 + 30p + -30p

Combine like terms: -7 + 7 = 0
-48 + -30p + 18p2 = 0 + 30p + -30p
-48 + -30p + 18p2 = 30p + -30p

Combine like terms: 30p + -30p = 0
-48 + -30p + 18p2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-8 + -5p + 3p2) = 0

Factor a trinomial.
6((-1 + -1p)(8 + -3p)) = 0

Ignore the factor 6.

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

Simplifying
-1 + -1p = 0

Solving
-1 + -1p = 0

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

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

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

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

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

Simplifying
p = -1

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 = {-1, 2.666666667}

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