(1+4y)(2y+3)=

Solution for (1+4y)(2y+3)= equation:

Simplifying
(1 + 4y)(2y + 3) = 0

Reorder the terms:
(1 + 4y)(3 + 2y) = 0

Multiply (1 + 4y) * (3 + 2y)
(1(3 + 2y) + 4y * (3 + 2y)) = 0
((3 * 1 + 2y * 1) + 4y * (3 + 2y)) = 0
((3 + 2y) + 4y * (3 + 2y)) = 0
(3 + 2y + (3 * 4y + 2y * 4y)) = 0
(3 + 2y + (12y + 8y2)) = 0

Combine like terms: 2y + 12y = 14y
(3 + 14y + 8y2) = 0

Solving
3 + 14y + 8y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3 + 2y)(1 + 4y) = 0

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

Simplifying
3 + 2y = 0

Solving
3 + 2y = 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 + 2y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2y = 0 + -3
2y = 0 + -3

Combine like terms: 0 + -3 = -3
2y = -3

Divide each side by '2'.
y = -1.5

Simplifying
y = -1.5
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 = {-1.5, -0.25}