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

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


Simplifying
(4u + 2)(7 + -1u) = 0

Reorder the terms:
(2 + 4u)(7 + -1u) = 0

Multiply (2 + 4u) * (7 + -1u)
(2(7 + -1u) + 4u * (7 + -1u)) = 0
((7 * 2 + -1u * 2) + 4u * (7 + -1u)) = 0
((14 + -2u) + 4u * (7 + -1u)) = 0
(14 + -2u + (7 * 4u + -1u * 4u)) = 0
(14 + -2u + (28u + -4u2)) = 0

Combine like terms: -2u + 28u = 26u
(14 + 26u + -4u2) = 0

Solving
14 + 26u + -4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 13u + -2u2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + -1u)' equal to zero and attempt to solve:

Simplifying
7 + -1u = 0

Solving
7 + -1u = 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 + -1u = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1u = 0 + -7
-1u = 0 + -7

Combine like terms: 0 + -7 = -7
-1u = -7

Divide each side by '-1'.
u = 7

Simplifying
u = 7

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 = {7, -0.5}

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