(1+u)(2u-3)=0

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Solution for (1+u)(2u-3)=0 equation:


Simplifying
(1 + u)(2u + -3) = 0

Reorder the terms:
(1 + u)(-3 + 2u) = 0

Multiply (1 + u) * (-3 + 2u)
(1(-3 + 2u) + u(-3 + 2u)) = 0
((-3 * 1 + 2u * 1) + u(-3 + 2u)) = 0
((-3 + 2u) + u(-3 + 2u)) = 0
(-3 + 2u + (-3 * u + 2u * u)) = 0
(-3 + 2u + (-3u + 2u2)) = 0

Combine like terms: 2u + -3u = -1u
(-3 + -1u + 2u2) = 0

Solving
-3 + -1u + 2u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-1 + -1u)(3 + -2u) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(3 + -2u)' equal to zero and attempt to solve: Simplifying 3 + -2u = 0 Solving 3 + -2u = 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 + -2u = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2u = 0 + -3 -2u = 0 + -3 Combine like terms: 0 + -3 = -3 -2u = -3 Divide each side by '-2'. u = 1.5 Simplifying u = 1.5

Solution

u = {-1, 1.5}

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