(4u-7)(2+u)=0

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Solution for (4u-7)(2+u)=0 equation:


Simplifying
(4u + -7)(2 + u) = 0

Reorder the terms:
(-7 + 4u)(2 + u) = 0

Multiply (-7 + 4u) * (2 + u)
(-7(2 + u) + 4u * (2 + u)) = 0
((2 * -7 + u * -7) + 4u * (2 + u)) = 0
((-14 + -7u) + 4u * (2 + u)) = 0
(-14 + -7u + (2 * 4u + u * 4u)) = 0
(-14 + -7u + (8u + 4u2)) = 0

Combine like terms: -7u + 8u = 1u
(-14 + 1u + 4u2) = 0

Solving
-14 + 1u + 4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-2 + -1u)(7 + -4u) = 0

Subproblem 1

Set the factor '(-2 + -1u)' equal to zero and attempt to solve: Simplifying -2 + -1u = 0 Solving -2 + -1u = 0 Move all terms containing u to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1u = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1u = 0 + 2 -1u = 0 + 2 Combine like terms: 0 + 2 = 2 -1u = 2 Divide each side by '-1'. u = -2 Simplifying u = -2

Subproblem 2

Set the factor '(7 + -4u)' equal to zero and attempt to solve: Simplifying 7 + -4u = 0 Solving 7 + -4u = 0 Move all terms containing u to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4u = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4u = 0 + -7 -4u = 0 + -7 Combine like terms: 0 + -7 = -7 -4u = -7 Divide each side by '-4'. u = 1.75 Simplifying u = 1.75

Solution

u = {-2, 1.75}

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