(p+3)(4p+1)=

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Solution for (p+3)(4p+1)= equation:


Simplifying
(p + 3)(4p + 1) = 0

Reorder the terms:
(3 + p)(4p + 1) = 0

Reorder the terms:
(3 + p)(1 + 4p) = 0

Multiply (3 + p) * (1 + 4p)
(3(1 + 4p) + p(1 + 4p)) = 0
((1 * 3 + 4p * 3) + p(1 + 4p)) = 0
((3 + 12p) + p(1 + 4p)) = 0
(3 + 12p + (1 * p + 4p * p)) = 0
(3 + 12p + (1p + 4p2)) = 0

Combine like terms: 12p + 1p = 13p
(3 + 13p + 4p2) = 0

Solving
3 + 13p + 4p2 = 0

Solving for variable 'p'.

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

Subproblem 1

Set the factor '(3 + p)' equal to zero and attempt to solve: Simplifying 3 + p = 0 Solving 3 + p = 0 Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + p = 0 + -3 p = 0 + -3 Combine like terms: 0 + -3 = -3 p = -3 Simplifying p = -3

Subproblem 2

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

Solution

p = {-3, -0.25}

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