4y(y+8)=7(y+8)

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Solution for 4y(y+8)=7(y+8) equation: 


Simplifying
4y(y + 8) = 7(y + 8)

Reorder the terms:
4y(8 + y) = 7(y + 8)
(8 * 4y + y * 4y) = 7(y + 8)
(32y + 4y2) = 7(y + 8)

Reorder the terms:
32y + 4y2 = 7(8 + y)
32y + 4y2 = (8 * 7 + y * 7)
32y + 4y2 = (56 + 7y)

Solving
32y + 4y2 = 56 + 7y

Solving for variable 'y'.

Reorder the terms:
-56 + 32y + -7y + 4y2 = 56 + 7y + -56 + -7y

Combine like terms: 32y + -7y = 25y
-56 + 25y + 4y2 = 56 + 7y + -56 + -7y

Reorder the terms:
-56 + 25y + 4y2 = 56 + -56 + 7y + -7y

Combine like terms: 56 + -56 = 0
-56 + 25y + 4y2 = 0 + 7y + -7y
-56 + 25y + 4y2 = 7y + -7y

Combine like terms: 7y + -7y = 0
-56 + 25y + 4y2 = 0

Factor a trinomial.
(-8 + -1y)(7 + -4y) = 0


Subproblem 1
Set the factor '(-8 + -1y)' equal to zero and attempt to solve:

Simplifying
-8 + -1y = 0

Solving
-8 + -1y = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1y = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1y = 0 + 8
-1y = 0 + 8

Combine like terms: 0 + 8 = 8
-1y = 8

Divide each side by '-1'.
y = -8

Simplifying
y = -8

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 = {-8, 1.75}

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