2u(u+1)+5(u+1)=

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Solution for 2u(u+1)+5(u+1)= equation:


Simplifying
2u(u + 1) + 5(u + 1) = 0

Reorder the terms:
2u(1 + u) + 5(u + 1) = 0
(1 * 2u + u * 2u) + 5(u + 1) = 0
(2u + 2u2) + 5(u + 1) = 0

Reorder the terms:
2u + 2u2 + 5(1 + u) = 0
2u + 2u2 + (1 * 5 + u * 5) = 0
2u + 2u2 + (5 + 5u) = 0

Reorder the terms:
5 + 2u + 5u + 2u2 = 0

Combine like terms: 2u + 5u = 7u
5 + 7u + 2u2 = 0

Solving
5 + 7u + 2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(5 + 2u)(1 + u) = 0

Subproblem 1

Set the factor '(5 + 2u)' equal to zero and attempt to solve: Simplifying 5 + 2u = 0 Solving 5 + 2u = 0 Move all terms containing u to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2u = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2u = 0 + -5 2u = 0 + -5 Combine like terms: 0 + -5 = -5 2u = -5 Divide each side by '2'. u = -2.5 Simplifying u = -2.5

Subproblem 2

Set the factor '(1 + u)' equal to zero and attempt to solve: Simplifying 1 + u = 0 Solving 1 + u = 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 + u = 0 + -1 Combine like terms: 1 + -1 = 0 0 + u = 0 + -1 u = 0 + -1 Combine like terms: 0 + -1 = -1 u = -1 Simplifying u = -1

Solution

u = {-2.5, -1}

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