6y(y+4)=7y-5

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Solution for 6y(y+4)=7y-5 equation: 


Simplifying
6y(y + 4) = 7y + -5

Reorder the terms:
6y(4 + y) = 7y + -5
(4 * 6y + y * 6y) = 7y + -5
(24y + 6y2) = 7y + -5

Reorder the terms:
24y + 6y2 = -5 + 7y

Solving
24y + 6y2 = -5 + 7y

Solving for variable 'y'.

Reorder the terms:
5 + 24y + -7y + 6y2 = -5 + 7y + 5 + -7y

Combine like terms: 24y + -7y = 17y
5 + 17y + 6y2 = -5 + 7y + 5 + -7y

Reorder the terms:
5 + 17y + 6y2 = -5 + 5 + 7y + -7y

Combine like terms: -5 + 5 = 0
5 + 17y + 6y2 = 0 + 7y + -7y
5 + 17y + 6y2 = 7y + -7y

Combine like terms: 7y + -7y = 0
5 + 17y + 6y2 = 0

Factor a trinomial.
(5 + 2y)(1 + 3y) = 0


Subproblem 1
Set the factor '(5 + 2y)' equal to zero and attempt to solve:

Simplifying
5 + 2y = 0

Solving
5 + 2y = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2y = 0 + -5
2y = 0 + -5

Combine like terms: 0 + -5 = -5
2y = -5

Divide each side by '2'.
y = -2.5

Simplifying
y = -2.5

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

Simplifying
1 + 3y = 0

Solving
1 + 3y = 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 + 3y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3y = 0 + -1
3y = 0 + -1

Combine like terms: 0 + -1 = -1
3y = -1

Divide each side by '3'.
y = -0.3333333333

Simplifying
y = -0.3333333333
Solution
y = {-2.5, -0.3333333333}

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