(y-7)(4y+17)=0

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Solution for (y-7)(4y+17)=0 equation: 


Simplifying
(y + -7)(4y + 17) = 0

Reorder the terms:
(-7 + y)(4y + 17) = 0

Reorder the terms:
(-7 + y)(17 + 4y) = 0

Multiply (-7 + y) * (17 + 4y)
(-7(17 + 4y) + y(17 + 4y)) = 0
((17 * -7 + 4y * -7) + y(17 + 4y)) = 0
((-119 + -28y) + y(17 + 4y)) = 0
(-119 + -28y + (17 * y + 4y * y)) = 0
(-119 + -28y + (17y + 4y2)) = 0

Combine like terms: -28y + 17y = -11y
(-119 + -11y + 4y2) = 0

Solving
-119 + -11y + 4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-17 + -4y)(7 + -1y) = 0


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 '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

Solving
7 + -1y = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1y = 0 + -7

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

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

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

Simplifying
y = 7
Solution
y = {-4.25, 7}

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