(3y+1)(2y-7)=0

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Solution for (3y+1)(2y-7)=0 equation: 


Simplifying
(3y + 1)(2y + -7) = 0

Reorder the terms:
(1 + 3y)(2y + -7) = 0

Reorder the terms:
(1 + 3y)(-7 + 2y) = 0

Multiply (1 + 3y) * (-7 + 2y)
(1(-7 + 2y) + 3y * (-7 + 2y)) = 0
((-7 * 1 + 2y * 1) + 3y * (-7 + 2y)) = 0
((-7 + 2y) + 3y * (-7 + 2y)) = 0
(-7 + 2y + (-7 * 3y + 2y * 3y)) = 0
(-7 + 2y + (-21y + 6y2)) = 0

Combine like terms: 2y + -21y = -19y
(-7 + -19y + 6y2) = 0

Solving
-7 + -19y + 6y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1 + -3y)(7 + -2y) = 0


Subproblem 1
Set the factor '(-1 + -3y)' equal to zero and attempt to solve:

Simplifying
-1 + -3y = 0

Solving
-1 + -3y = 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 + -3y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3y = 0 + 1
-3y = 0 + 1

Combine like terms: 0 + 1 = 1
-3y = 1

Divide each side by '-3'.
y = -0.3333333333

Simplifying
y = -0.3333333333

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

Simplifying
7 + -2y = 0

Solving
7 + -2y = 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 + -2y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2y = 0 + -7
-2y = 0 + -7

Combine like terms: 0 + -7 = -7
-2y = -7

Divide each side by '-2'.
y = 3.5

Simplifying
y = 3.5
Solution
y = {-0.3333333333, 3.5}

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