5y(2y-3)+(2y+3)=

Solution for 5y(2y-3)+(2y+3)= equation:

Simplifying
5y(2y + -3) + (2y + 3) = 0

Reorder the terms:
5y(-3 + 2y) + (2y + 3) = 0
(-3 * 5y + 2y * 5y) + (2y + 3) = 0
(-15y + 10y2) + (2y + 3) = 0

Reorder the terms:
-15y + 10y2 + (3 + 2y) = 0

Remove parenthesis around (3 + 2y)
-15y + 10y2 + 3 + 2y = 0

Reorder the terms:
3 + -15y + 2y + 10y2 = 0

Combine like terms: -15y + 2y = -13y
3 + -13y + 10y2 = 0

Solving
3 + -13y + 10y2 = 0

Solving for variable 'y'.

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

Subproblem 1
Set the factor '(3 + -10y)' equal to zero and attempt to solve:

Simplifying
3 + -10y = 0

Solving
3 + -10y = 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 + -10y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -10y = 0 + -3
-10y = 0 + -3

Combine like terms: 0 + -3 = -3
-10y = -3

Divide each side by '-10'.
y = 0.3

Simplifying
y = 0.3
Subproblem 2
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

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

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

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

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

Simplifying
y = 1
Solution
y = {0.3, 1}