7y^2-[-5y-(4y^2-8y)]-[2+(17y-2)]=0

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Solution for 7y^2-[-5y-(4y^2-8y)]-[2+(17y-2)]=0 equation: 


Simplifying
7y2 + -1[-5y + -1(4y2 + -8y)] + -1[2 + (17y + -2)] = 0

Reorder the terms:
7y2 + -1[-5y + -1(-8y + 4y2)] + -1[2 + (17y + -2)] = 0
7y2 + -1[-5y + (-8y * -1 + 4y2 * -1)] + -1[2 + (17y + -2)] = 0
7y2 + -1[-5y + (8y + -4y2)] + -1[2 + (17y + -2)] = 0

Combine like terms: -5y + 8y = 3y
7y2 + -1[3y + -4y2] + -1[2 + (17y + -2)] = 0
7y2 + [3y * -1 + -4y2 * -1] + -1[2 + (17y + -2)] = 0
7y2 + [-3y + 4y2] + -1[2 + (17y + -2)] = 0

Reorder the terms:
7y2 + -3y + 4y2 + -1[2 + (-2 + 17y)] = 0

Remove parenthesis around (-2 + 17y)
7y2 + -3y + 4y2 + -1[2 + -2 + 17y] = 0

Combine like terms: 2 + -2 = 0
7y2 + -3y + 4y2 + -1[0 + 17y] = 0
7y2 + -3y + 4y2 + -1[17y] = 0

Remove brackets around [17y]
7y2 + -3y + 4y2 + -1 * 17y = 0

Multiply -1 * 17
7y2 + -3y + 4y2 + -17y = 0

Reorder the terms:
-3y + -17y + 7y2 + 4y2 = 0

Combine like terms: -3y + -17y = -20y
-20y + 7y2 + 4y2 = 0

Combine like terms: 7y2 + 4y2 = 11y2
-20y + 11y2 = 0

Solving
-20y + 11y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-20 + 11y) = 0


Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

Subproblem 2
Set the factor '(-20 + 11y)' equal to zero and attempt to solve:

Simplifying
-20 + 11y = 0

Solving
-20 + 11y = 0

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

Add '20' to each side of the equation.
-20 + 20 + 11y = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 11y = 0 + 20
11y = 0 + 20

Combine like terms: 0 + 20 = 20
11y = 20

Divide each side by '11'.
y = 1.818181818

Simplifying
y = 1.818181818
Solution
y = {0, 1.818181818}

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