(4u-7)(5+u)=0

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Solution for (4u-7)(5+u)=0 equation:


Simplifying
(4u + -7)(5 + u) = 0

Reorder the terms:
(-7 + 4u)(5 + u) = 0

Multiply (-7 + 4u) * (5 + u)
(-7(5 + u) + 4u * (5 + u)) = 0
((5 * -7 + u * -7) + 4u * (5 + u)) = 0
((-35 + -7u) + 4u * (5 + u)) = 0
(-35 + -7u + (5 * 4u + u * 4u)) = 0
(-35 + -7u + (20u + 4u2)) = 0

Combine like terms: -7u + 20u = 13u
(-35 + 13u + 4u2) = 0

Solving
-35 + 13u + 4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-5 + -1u)(7 + -4u) = 0

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 '(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 = {-5, 1.75}

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