(u-4)(u-4)=2u^2-3u+10

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Solution for (u-4)(u-4)=2u^2-3u+10 equation: 


Simplifying
(u + -4)(u + -4) = 2u2 + -3u + 10

Reorder the terms:
(-4 + u)(u + -4) = 2u2 + -3u + 10

Reorder the terms:
(-4 + u)(-4 + u) = 2u2 + -3u + 10

Multiply (-4 + u) * (-4 + u)
(-4(-4 + u) + u(-4 + u)) = 2u2 + -3u + 10
((-4 * -4 + u * -4) + u(-4 + u)) = 2u2 + -3u + 10
((16 + -4u) + u(-4 + u)) = 2u2 + -3u + 10
(16 + -4u + (-4 * u + u * u)) = 2u2 + -3u + 10
(16 + -4u + (-4u + u2)) = 2u2 + -3u + 10

Combine like terms: -4u + -4u = -8u
(16 + -8u + u2) = 2u2 + -3u + 10

Reorder the terms:
16 + -8u + u2 = 10 + -3u + 2u2

Solving
16 + -8u + u2 = 10 + -3u + 2u2

Solving for variable 'u'.

Reorder the terms:
16 + -10 + -8u + 3u + u2 + -2u2 = 10 + -3u + 2u2 + -10 + 3u + -2u2

Combine like terms: 16 + -10 = 6
6 + -8u + 3u + u2 + -2u2 = 10 + -3u + 2u2 + -10 + 3u + -2u2

Combine like terms: -8u + 3u = -5u
6 + -5u + u2 + -2u2 = 10 + -3u + 2u2 + -10 + 3u + -2u2

Combine like terms: u2 + -2u2 = -1u2
6 + -5u + -1u2 = 10 + -3u + 2u2 + -10 + 3u + -2u2

Reorder the terms:
6 + -5u + -1u2 = 10 + -10 + -3u + 3u + 2u2 + -2u2

Combine like terms: 10 + -10 = 0
6 + -5u + -1u2 = 0 + -3u + 3u + 2u2 + -2u2
6 + -5u + -1u2 = -3u + 3u + 2u2 + -2u2

Combine like terms: -3u + 3u = 0
6 + -5u + -1u2 = 0 + 2u2 + -2u2
6 + -5u + -1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
6 + -5u + -1u2 = 0

Factor a trinomial.
(1 + -1u)(6 + u) = 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 '(6 + u)' equal to zero and attempt to solve:

Simplifying
6 + u = 0

Solving
6 + u = 0

Move all terms containing u to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + u = 0 + -6

Combine like terms: 6 + -6 = 0
0 + u = 0 + -6
u = 0 + -6

Combine like terms: 0 + -6 = -6
u = -6

Simplifying
u = -6
Solution
u = {1, -6}

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