(4u-2)(5+u)=0

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Solution for (4u-2)(5+u)=0 equation:


Simplifying
(4u + -2)(5 + u) = 0

Reorder the terms:
(-2 + 4u)(5 + u) = 0

Multiply (-2 + 4u) * (5 + u)
(-2(5 + u) + 4u * (5 + u)) = 0
((5 * -2 + u * -2) + 4u * (5 + u)) = 0
((-10 + -2u) + 4u * (5 + u)) = 0
(-10 + -2u + (5 * 4u + u * 4u)) = 0
(-10 + -2u + (20u + 4u2)) = 0

Combine like terms: -2u + 20u = 18u
(-10 + 18u + 4u2) = 0

Solving
-10 + 18u + 4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 9u + 2u2) = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(-5 + -1u)' equal to zero and attempt to solve: Simplifying -5 + -1u = 0 Solving -5 + -1u = 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 + -1u = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1u = 0 + 5 -1u = 0 + 5 Combine like terms: 0 + 5 = 5 -1u = 5 Divide each side by '-1'. u = -5 Simplifying u = -5

Subproblem 2

Set the factor '(1 + -2u)' equal to zero and attempt to solve: Simplifying 1 + -2u = 0 Solving 1 + -2u = 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 + -2u = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2u = 0 + -1 -2u = 0 + -1 Combine like terms: 0 + -1 = -1 -2u = -1 Divide each side by '-2'. u = 0.5 Simplifying u = 0.5

Solution

u = {-5, 0.5}

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