16p^2-24p+9=12p+1

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Solution for 16p^2-24p+9=12p+1 equation: 


Simplifying
16p2 + -24p + 9 = 12p + 1

Reorder the terms:
9 + -24p + 16p2 = 12p + 1

Reorder the terms:
9 + -24p + 16p2 = 1 + 12p

Solving
9 + -24p + 16p2 = 1 + 12p

Solving for variable 'p'.

Reorder the terms:
9 + -1 + -24p + -12p + 16p2 = 1 + 12p + -1 + -12p

Combine like terms: 9 + -1 = 8
8 + -24p + -12p + 16p2 = 1 + 12p + -1 + -12p

Combine like terms: -24p + -12p = -36p
8 + -36p + 16p2 = 1 + 12p + -1 + -12p

Reorder the terms:
8 + -36p + 16p2 = 1 + -1 + 12p + -12p

Combine like terms: 1 + -1 = 0
8 + -36p + 16p2 = 0 + 12p + -12p
8 + -36p + 16p2 = 12p + -12p

Combine like terms: 12p + -12p = 0
8 + -36p + 16p2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + -9p + 4p2) = 0

Factor a trinomial.
4((1 + -4p)(2 + -1p)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(1 + -4p)' equal to zero and attempt to solve:

Simplifying
1 + -4p = 0

Solving
1 + -4p = 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 + -4p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4p = 0 + -1
-4p = 0 + -1

Combine like terms: 0 + -1 = -1
-4p = -1

Divide each side by '-4'.
p = 0.25

Simplifying
p = 0.25

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 = {0.25, 2}

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