p(4p+7)(4p-7)=0

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Solution for p(4p+7)(4p-7)=0 equation: 


Simplifying
p(4p + 7)(4p + -7) = 0

Reorder the terms:
p(7 + 4p)(4p + -7) = 0

Reorder the terms:
p(7 + 4p)(-7 + 4p) = 0

Multiply (7 + 4p) * (-7 + 4p)
p(7(-7 + 4p) + 4p * (-7 + 4p)) = 0
p((-7 * 7 + 4p * 7) + 4p * (-7 + 4p)) = 0
p((-49 + 28p) + 4p * (-7 + 4p)) = 0
p(-49 + 28p + (-7 * 4p + 4p * 4p)) = 0
p(-49 + 28p + (-28p + 16p2)) = 0

Combine like terms: 28p + -28p = 0
p(-49 + 0 + 16p2) = 0
p(-49 + 16p2) = 0
(-49 * p + 16p2 * p) = 0
(-49p + 16p3) = 0

Solving
-49p + 16p3 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'p'.
p(-49 + 16p2) = 0

Factor a difference between two squares.
p((7 + 4p)(-7 + 4p)) = 0


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 '(7 + 4p)' equal to zero and attempt to solve:

Simplifying
7 + 4p = 0

Solving
7 + 4p = 0

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

Add '-7' to each side of the equation.
7 + -7 + 4p = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4p = 0 + -7
4p = 0 + -7

Combine like terms: 0 + -7 = -7
4p = -7

Divide each side by '4'.
p = -1.75

Simplifying
p = -1.75

Subproblem 3
Set the factor '(-7 + 4p)' equal to zero and attempt to solve:

Simplifying
-7 + 4p = 0

Solving
-7 + 4p = 0

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

Add '7' to each side of the equation.
-7 + 7 + 4p = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 4p = 0 + 7
4p = 0 + 7

Combine like terms: 0 + 7 = 7
4p = 7

Divide each side by '4'.
p = 1.75

Simplifying
p = 1.75
Solution
p = {0, -1.75, 1.75}

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