(y+1)(4y-25)=(2y-5)(2y-8)

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Solution for (y+1)(4y-25)=(2y-5)(2y-8) equation: 


Simplifying
(y + 1)(4y + -25) = (2y + -5)(2y + -8)

Reorder the terms:
(1 + y)(4y + -25) = (2y + -5)(2y + -8)

Reorder the terms:
(1 + y)(-25 + 4y) = (2y + -5)(2y + -8)

Multiply (1 + y) * (-25 + 4y)
(1(-25 + 4y) + y(-25 + 4y)) = (2y + -5)(2y + -8)
((-25 * 1 + 4y * 1) + y(-25 + 4y)) = (2y + -5)(2y + -8)
((-25 + 4y) + y(-25 + 4y)) = (2y + -5)(2y + -8)
(-25 + 4y + (-25 * y + 4y * y)) = (2y + -5)(2y + -8)
(-25 + 4y + (-25y + 4y2)) = (2y + -5)(2y + -8)

Combine like terms: 4y + -25y = -21y
(-25 + -21y + 4y2) = (2y + -5)(2y + -8)

Reorder the terms:
-25 + -21y + 4y2 = (-5 + 2y)(2y + -8)

Reorder the terms:
-25 + -21y + 4y2 = (-5 + 2y)(-8 + 2y)

Multiply (-5 + 2y) * (-8 + 2y)
-25 + -21y + 4y2 = (-5(-8 + 2y) + 2y * (-8 + 2y))
-25 + -21y + 4y2 = ((-8 * -5 + 2y * -5) + 2y * (-8 + 2y))
-25 + -21y + 4y2 = ((40 + -10y) + 2y * (-8 + 2y))
-25 + -21y + 4y2 = (40 + -10y + (-8 * 2y + 2y * 2y))
-25 + -21y + 4y2 = (40 + -10y + (-16y + 4y2))

Combine like terms: -10y + -16y = -26y
-25 + -21y + 4y2 = (40 + -26y + 4y2)

Add '-4y2' to each side of the equation.
-25 + -21y + 4y2 + -4y2 = 40 + -26y + 4y2 + -4y2

Combine like terms: 4y2 + -4y2 = 0
-25 + -21y + 0 = 40 + -26y + 4y2 + -4y2
-25 + -21y = 40 + -26y + 4y2 + -4y2

Combine like terms: 4y2 + -4y2 = 0
-25 + -21y = 40 + -26y + 0
-25 + -21y = 40 + -26y

Solving
-25 + -21y = 40 + -26y

Solving for variable 'y'.

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

Add '26y' to each side of the equation.
-25 + -21y + 26y = 40 + -26y + 26y

Combine like terms: -21y + 26y = 5y
-25 + 5y = 40 + -26y + 26y

Combine like terms: -26y + 26y = 0
-25 + 5y = 40 + 0
-25 + 5y = 40

Add '25' to each side of the equation.
-25 + 25 + 5y = 40 + 25

Combine like terms: -25 + 25 = 0
0 + 5y = 40 + 25
5y = 40 + 25

Combine like terms: 40 + 25 = 65
5y = 65

Divide each side by '5'.
y = 13

Simplifying
y = 13

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