(12y+3)(y-4)=

Solution for (12y+3)(y-4)= equation:

Simplifying
(12y + 3)(y + -4) = 0

Reorder the terms:
(3 + 12y)(y + -4) = 0

Reorder the terms:
(3 + 12y)(-4 + y) = 0

Multiply (3 + 12y) * (-4 + y)
(3(-4 + y) + 12y * (-4 + y)) = 0
((-4 * 3 + y * 3) + 12y * (-4 + y)) = 0
((-12 + 3y) + 12y * (-4 + y)) = 0
(-12 + 3y + (-4 * 12y + y * 12y)) = 0
(-12 + 3y + (-48y + 12y2)) = 0

Combine like terms: 3y + -48y = -45y
(-12 + -45y + 12y2) = 0

Solving
-12 + -45y + 12y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + -15y + 4y2) = 0

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

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

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

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

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

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {-0.25, 4}