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

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


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

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

Multiply (-7 + 4Y) * (1 + Y)
(-7(1 + Y) + 4Y * (1 + Y)) = 0
((1 * -7 + Y * -7) + 4Y * (1 + Y)) = 0
((-7 + -7Y) + 4Y * (1 + Y)) = 0
(-7 + -7Y + (1 * 4Y + Y * 4Y)) = 0
(-7 + -7Y + (4Y + 4Y2)) = 0

Combine like terms: -7Y + 4Y = -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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