3(u-4)(u-4)+5=32

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Solution for 3(u-4)(u-4)+5=32 equation: 


Simplifying
3(u + -4)(u + -4) + 5 = 32

Reorder the terms:
3(-4 + u)(u + -4) + 5 = 32

Reorder the terms:
3(-4 + u)(-4 + u) + 5 = 32

Multiply (-4 + u) * (-4 + u)
3(-4(-4 + u) + u(-4 + u)) + 5 = 32
3((-4 * -4 + u * -4) + u(-4 + u)) + 5 = 32
3((16 + -4u) + u(-4 + u)) + 5 = 32
3(16 + -4u + (-4 * u + u * u)) + 5 = 32
3(16 + -4u + (-4u + u2)) + 5 = 32

Combine like terms: -4u + -4u = -8u
3(16 + -8u + u2) + 5 = 32
(16 * 3 + -8u * 3 + u2 * 3) + 5 = 32
(48 + -24u + 3u2) + 5 = 32

Reorder the terms:
48 + 5 + -24u + 3u2 = 32

Combine like terms: 48 + 5 = 53
53 + -24u + 3u2 = 32

Solving
53 + -24u + 3u2 = 32

Solving for variable 'u'.

Reorder the terms:
53 + -32 + -24u + 3u2 = 32 + -32

Combine like terms: 53 + -32 = 21
21 + -24u + 3u2 = 32 + -32

Combine like terms: 32 + -32 = 0
21 + -24u + 3u2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(7 + -8u + u2) = 0

Factor a trinomial.
3((1 + -1u)(7 + -1u)) = 0

Ignore the factor 3.

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 '(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
Solution
u = {1, 7}

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