(1-y)(4y+7)=0

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Solution for (1-y)(4y+7)=0 equation: 


Simplifying
(1 + -1y)(4y + 7) = 0

Reorder the terms:
(1 + -1y)(7 + 4y) = 0

Multiply (1 + -1y) * (7 + 4y)
(1(7 + 4y) + -1y * (7 + 4y)) = 0
((7 * 1 + 4y * 1) + -1y * (7 + 4y)) = 0
((7 + 4y) + -1y * (7 + 4y)) = 0
(7 + 4y + (7 * -1y + 4y * -1y)) = 0
(7 + 4y + (-7y + -4y2)) = 0

Combine like terms: 4y + -7y = -3y
(7 + -3y + -4y2) = 0

Solving
7 + -3y + -4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(1 + -1y)(7 + 4y) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + 4y)' equal to zero and attempt to solve:

Simplifying
7 + 4y = 0

Solving
7 + 4y = 0

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

Add '-7' to each side of the equation.
7 + -7 + 4y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4y = 0 + -7
4y = 0 + -7

Combine like terms: 0 + -7 = -7
4y = -7

Divide each side by '4'.
y = -1.75

Simplifying
y = -1.75
Solution
y = {1, -1.75}

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