4y(y+6)=7(y+6)

Solution for 4y(y+6)=7(y+6) equation:

Simplifying
4y(y + 6) = 7(y + 6)

Reorder the terms:
4y(6 + y) = 7(y + 6)
(6 * 4y + y * 4y) = 7(y + 6)
(24y + 4y2) = 7(y + 6)

Reorder the terms:
24y + 4y2 = 7(6 + y)
24y + 4y2 = (6 * 7 + y * 7)
24y + 4y2 = (42 + 7y)

Solving
24y + 4y2 = 42 + 7y

Solving for variable 'y'.

Reorder the terms:
-42 + 24y + -7y + 4y2 = 42 + 7y + -42 + -7y

Combine like terms: 24y + -7y = 17y
-42 + 17y + 4y2 = 42 + 7y + -42 + -7y

Reorder the terms:
-42 + 17y + 4y2 = 42 + -42 + 7y + -7y

Combine like terms: 42 + -42 = 0
-42 + 17y + 4y2 = 0 + 7y + -7y
-42 + 17y + 4y2 = 7y + -7y

Combine like terms: 7y + -7y = 0
-42 + 17y + 4y2 = 0

Factor a trinomial.
(-6 + -1y)(7 + -4y) = 0

Subproblem 1
Set the factor '(-6 + -1y)' equal to zero and attempt to solve:

Simplifying
-6 + -1y = 0

Solving
-6 + -1y = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1y = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1y = 0 + 6
-1y = 0 + 6

Combine like terms: 0 + 6 = 6
-1y = 6

Divide each side by '-1'.
y = -6

Simplifying
y = -6
Subproblem 2
Set the factor '(7 + -4y)' equal to zero and attempt to solve:

Simplifying
7 + -4y = 0

Solving
7 + -4y = 0

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

Add '-7' to each side of the equation.
7 + -7 + -4y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4y = 0 + -7
-4y = 0 + -7

Combine like terms: 0 + -7 = -7
-4y = -7

Divide each side by '-4'.
y = 1.75

Simplifying
y = 1.75
Solution
y = {-6, 1.75}