=(17+4y)(4+y)

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Solution for =(17+4y)(4+y) equation: 


Simplifying
0 = (17 + 4y)(4 + y)

Multiply (17 + 4y) * (4 + y)
0 = (17(4 + y) + 4y * (4 + y))
0 = ((4 * 17 + y * 17) + 4y * (4 + y))
0 = ((68 + 17y) + 4y * (4 + y))
0 = (68 + 17y + (4 * 4y + y * 4y))
0 = (68 + 17y + (16y + 4y2))

Combine like terms: 17y + 16y = 33y
0 = (68 + 33y + 4y2)

Solving
0 = 68 + 33y + 4y2

Solving for variable 'y'.

Combine like terms: 0 + -68 = -68
-68 + -33y + -4y2 = 68 + 33y + 4y2 + -68 + -33y + -4y2

Reorder the terms:
-68 + -33y + -4y2 = 68 + -68 + 33y + -33y + 4y2 + -4y2

Combine like terms: 68 + -68 = 0
-68 + -33y + -4y2 = 0 + 33y + -33y + 4y2 + -4y2
-68 + -33y + -4y2 = 33y + -33y + 4y2 + -4y2

Combine like terms: 33y + -33y = 0
-68 + -33y + -4y2 = 0 + 4y2 + -4y2
-68 + -33y + -4y2 = 4y2 + -4y2

Combine like terms: 4y2 + -4y2 = 0
-68 + -33y + -4y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(68 + 33y + 4y2) = 0

Factor a trinomial.
-1((17 + 4y)(4 + y)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(17 + 4y)' equal to zero and attempt to solve:

Simplifying
17 + 4y = 0

Solving
17 + 4y = 0

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

Add '-17' to each side of the equation.
17 + -17 + 4y = 0 + -17

Combine like terms: 17 + -17 = 0
0 + 4y = 0 + -17
4y = 0 + -17

Combine like terms: 0 + -17 = -17
4y = -17

Divide each side by '4'.
y = -4.25

Simplifying
y = -4.25

Subproblem 2
Set the factor '(4 + y)' equal to zero and attempt to solve:

Simplifying
4 + y = 0

Solving
4 + y = 0

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

Add '-4' to each side of the equation.
4 + -4 + y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + y = 0 + -4
y = 0 + -4

Combine like terms: 0 + -4 = -4
y = -4

Simplifying
y = -4
Solution
y = {-4.25, -4}

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