(2y+1)(3y-5)-2y(y-4)=

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Solution for (2y+1)(3y-5)-2y(y-4)= equation:


Simplifying
(2y + 1)(3y + -5) + -2y(y + -4) = 0

Reorder the terms:
(1 + 2y)(3y + -5) + -2y(y + -4) = 0

Reorder the terms:
(1 + 2y)(-5 + 3y) + -2y(y + -4) = 0

Multiply (1 + 2y) * (-5 + 3y)
(1(-5 + 3y) + 2y * (-5 + 3y)) + -2y(y + -4) = 0
((-5 * 1 + 3y * 1) + 2y * (-5 + 3y)) + -2y(y + -4) = 0
((-5 + 3y) + 2y * (-5 + 3y)) + -2y(y + -4) = 0
(-5 + 3y + (-5 * 2y + 3y * 2y)) + -2y(y + -4) = 0
(-5 + 3y + (-10y + 6y2)) + -2y(y + -4) = 0

Combine like terms: 3y + -10y = -7y
(-5 + -7y + 6y2) + -2y(y + -4) = 0

Reorder the terms:
-5 + -7y + 6y2 + -2y(-4 + y) = 0
-5 + -7y + 6y2 + (-4 * -2y + y * -2y) = 0
-5 + -7y + 6y2 + (8y + -2y2) = 0

Reorder the terms:
-5 + -7y + 8y + 6y2 + -2y2 = 0

Combine like terms: -7y + 8y = 1y
-5 + 1y + 6y2 + -2y2 = 0

Combine like terms: 6y2 + -2y2 = 4y2
-5 + 1y + 4y2 = 0

Solving
-5 + 1y + 4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-5 + -4y)(1 + -1y) = 0

Subproblem 1

Set the factor '(-5 + -4y)' equal to zero and attempt to solve: Simplifying -5 + -4y = 0 Solving -5 + -4y = 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 + -4y = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4y = 0 + 5 -4y = 0 + 5 Combine like terms: 0 + 5 = 5 -4y = 5 Divide each side by '-4'. y = -1.25 Simplifying y = -1.25

Subproblem 2

Set the factor '(1 + -1y)' equal to zero and attempt to solve: Simplifying 1 + -1y = 0 Solving 1 + -1y = 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 + -1y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1y = 0 + -1 -1y = 0 + -1 Combine like terms: 0 + -1 = -1 -1y = -1 Divide each side by '-1'. y = 1 Simplifying y = 1

Solution

y = {-1.25, 1}

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