-5(2y+1)-11=4(y+7)2y

Solution for -5(2y+1)-11=4(y+7)2y equation:

Simplifying
-5(2y + 1) + -11 = 4(y + 7) * 2y

Reorder the terms:
-5(1 + 2y) + -11 = 4(y + 7) * 2y
(1 * -5 + 2y * -5) + -11 = 4(y + 7) * 2y
(-5 + -10y) + -11 = 4(y + 7) * 2y

Reorder the terms:
-5 + -11 + -10y = 4(y + 7) * 2y

Combine like terms: -5 + -11 = -16
-16 + -10y = 4(y + 7) * 2y

Reorder the terms:
-16 + -10y = 4(7 + y) * 2y

Reorder the terms for easier multiplication:
-16 + -10y = 4 * 2y(7 + y)

Multiply 4 * 2
-16 + -10y = 8y(7 + y)
-16 + -10y = (7 * 8y + y * 8y)
-16 + -10y = (56y + 8y2)

Solving
-16 + -10y = 56y + 8y2

Solving for variable 'y'.

Combine like terms: -10y + -56y = -66y
-16 + -66y + -8y2 = 56y + 8y2 + -56y + -8y2

Reorder the terms:
-16 + -66y + -8y2 = 56y + -56y + 8y2 + -8y2

Combine like terms: 56y + -56y = 0
-16 + -66y + -8y2 = 0 + 8y2 + -8y2
-16 + -66y + -8y2 = 8y2 + -8y2

Combine like terms: 8y2 + -8y2 = 0
-16 + -66y + -8y2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(8 + 33y + 4y2) = 0

Factor a trinomial.
-2((8 + y)(1 + 4y)) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(8 + y)' equal to zero and attempt to solve:

Simplifying
8 + y = 0

Solving
8 + y = 0

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

Add '-8' to each side of the equation.
8 + -8 + y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + y = 0 + -8
y = 0 + -8

Combine like terms: 0 + -8 = -8
y = -8

Simplifying
y = -8
Subproblem 2
Set the factor '(1 + 4y)' equal to zero and attempt to solve:

Simplifying
1 + 4y = 0

Solving
1 + 4y = 0

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

Add '-1' to each side of the equation.
1 + -1 + 4y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4y = 0 + -1
4y = 0 + -1

Combine like terms: 0 + -1 = -1
4y = -1

Divide each side by '4'.
y = -0.25

Simplifying
y = -0.25
Solution
y = {-8, -0.25}