(4u+1)(3+u)=0

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Solution for (4u+1)(3+u)=0 equation:


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

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

Multiply (1 + 4u) * (3 + u)
(1(3 + u) + 4u * (3 + u)) = 0
((3 * 1 + u * 1) + 4u * (3 + u)) = 0
((3 + 1u) + 4u * (3 + u)) = 0
(3 + 1u + (3 * 4u + u * 4u)) = 0
(3 + 1u + (12u + 4u2)) = 0

Combine like terms: 1u + 12u = 13u
(3 + 13u + 4u2) = 0

Solving
3 + 13u + 4u2 = 0

Solving for variable 'u'.

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

Subproblem 1

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

Subproblem 2

Set the factor '(1 + 4u)' equal to zero and attempt to solve: Simplifying 1 + 4u = 0 Solving 1 + 4u = 0 Move all terms containing u to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 4u = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4u = 0 + -1 4u = 0 + -1 Combine like terms: 0 + -1 = -1 4u = -1 Divide each side by '4'. u = -0.25 Simplifying u = -0.25

Solution

u = {-3, -0.25}

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