2-10y(5y+8)=32

Solution for 2-10y(5y+8)=32 equation:

Simplifying
2 + -10y(5y + 8) = 32

Reorder the terms:
2 + -10y(8 + 5y) = 32
2 + (8 * -10y + 5y * -10y) = 32
2 + (-80y + -50y2) = 32

Solving
2 + -80y + -50y2 = 32

Solving for variable 'y'.

Reorder the terms:
2 + -32 + -80y + -50y2 = 32 + -32

Combine like terms: 2 + -32 = -30
-30 + -80y + -50y2 = 32 + -32

Combine like terms: 32 + -32 = 0
-30 + -80y + -50y2 = 0

Factor out the Greatest Common Factor (GCF), '-10'.
-10(3 + 8y + 5y2) = 0

Factor a trinomial.
-10((1 + y)(3 + 5y)) = 0

Ignore the factor -10.
Subproblem 1
Set the factor '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

Solving
1 + y = 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 + y = 0 + -1

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

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

Simplifying
y = -1
Subproblem 2
Set the factor '(3 + 5y)' equal to zero and attempt to solve:

Simplifying
3 + 5y = 0

Solving
3 + 5y = 0

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

Add '-3' to each side of the equation.
3 + -3 + 5y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5y = 0 + -3
5y = 0 + -3

Combine like terms: 0 + -3 = -3
5y = -3

Divide each side by '5'.
y = -0.6

Simplifying
y = -0.6
Solution
y = {-1, -0.6}