(y+4)(y+14)-y(y+10)=216

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Solution for (y+4)(y+14)-y(y+10)=216 equation:


Simplifying
(y + 4)(y + 14) + -1y(y + 10) = 216

Reorder the terms:
(4 + y)(y + 14) + -1y(y + 10) = 216

Reorder the terms:
(4 + y)(14 + y) + -1y(y + 10) = 216

Multiply (4 + y) * (14 + y)
(4(14 + y) + y(14 + y)) + -1y(y + 10) = 216
((14 * 4 + y * 4) + y(14 + y)) + -1y(y + 10) = 216
((56 + 4y) + y(14 + y)) + -1y(y + 10) = 216
(56 + 4y + (14 * y + y * y)) + -1y(y + 10) = 216
(56 + 4y + (14y + y2)) + -1y(y + 10) = 216

Combine like terms: 4y + 14y = 18y
(56 + 18y + y2) + -1y(y + 10) = 216

Reorder the terms:
56 + 18y + y2 + -1y(10 + y) = 216
56 + 18y + y2 + (10 * -1y + y * -1y) = 216
56 + 18y + y2 + (-10y + -1y2) = 216

Reorder the terms:
56 + 18y + -10y + y2 + -1y2 = 216

Combine like terms: 18y + -10y = 8y
56 + 8y + y2 + -1y2 = 216

Combine like terms: y2 + -1y2 = 0
56 + 8y + 0 = 216
56 + 8y = 216

Solving
56 + 8y = 216

Solving for variable 'y'.

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

Add '-56' to each side of the equation.
56 + -56 + 8y = 216 + -56

Combine like terms: 56 + -56 = 0
0 + 8y = 216 + -56
8y = 216 + -56

Combine like terms: 216 + -56 = 160
8y = 160

Divide each side by '8'.
y = 20

Simplifying
y = 20

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