y(10y+9)=7+(5y-1)(2y+3)

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Solution for y(10y+9)=7+(5y-1)(2y+3) equation:


Simplifying
y(10y + 9) = 7 + (5y + -1)(2y + 3)

Reorder the terms:
y(9 + 10y) = 7 + (5y + -1)(2y + 3)
(9 * y + 10y * y) = 7 + (5y + -1)(2y + 3)
(9y + 10y2) = 7 + (5y + -1)(2y + 3)

Reorder the terms:
9y + 10y2 = 7 + (-1 + 5y)(2y + 3)

Reorder the terms:
9y + 10y2 = 7 + (-1 + 5y)(3 + 2y)

Multiply (-1 + 5y) * (3 + 2y)
9y + 10y2 = 7 + (-1(3 + 2y) + 5y * (3 + 2y))
9y + 10y2 = 7 + ((3 * -1 + 2y * -1) + 5y * (3 + 2y))
9y + 10y2 = 7 + ((-3 + -2y) + 5y * (3 + 2y))
9y + 10y2 = 7 + (-3 + -2y + (3 * 5y + 2y * 5y))
9y + 10y2 = 7 + (-3 + -2y + (15y + 10y2))

Combine like terms: -2y + 15y = 13y
9y + 10y2 = 7 + (-3 + 13y + 10y2)

Combine like terms: 7 + -3 = 4
9y + 10y2 = 4 + 13y + 10y2

Add '-10y2' to each side of the equation.
9y + 10y2 + -10y2 = 4 + 13y + 10y2 + -10y2

Combine like terms: 10y2 + -10y2 = 0
9y + 0 = 4 + 13y + 10y2 + -10y2
9y = 4 + 13y + 10y2 + -10y2

Combine like terms: 10y2 + -10y2 = 0
9y = 4 + 13y + 0
9y = 4 + 13y

Solving
9y = 4 + 13y

Solving for variable 'y'.

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

Add '-13y' to each side of the equation.
9y + -13y = 4 + 13y + -13y

Combine like terms: 9y + -13y = -4y
-4y = 4 + 13y + -13y

Combine like terms: 13y + -13y = 0
-4y = 4 + 0
-4y = 4

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

Simplifying
y = -1

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