(2y-7)(3y+4)=0

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Solution for (2y-7)(3y+4)=0 equation: 


Simplifying
(2y + -7)(3y + 4) = 0

Reorder the terms:
(-7 + 2y)(3y + 4) = 0

Reorder the terms:
(-7 + 2y)(4 + 3y) = 0

Multiply (-7 + 2y) * (4 + 3y)
(-7(4 + 3y) + 2y * (4 + 3y)) = 0
((4 * -7 + 3y * -7) + 2y * (4 + 3y)) = 0
((-28 + -21y) + 2y * (4 + 3y)) = 0
(-28 + -21y + (4 * 2y + 3y * 2y)) = 0
(-28 + -21y + (8y + 6y2)) = 0

Combine like terms: -21y + 8y = -13y
(-28 + -13y + 6y2) = 0

Solving
-28 + -13y + 6y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-4 + -3y)(7 + -2y) = 0


Subproblem 1
Set the factor '(-4 + -3y)' equal to zero and attempt to solve:

Simplifying
-4 + -3y = 0

Solving
-4 + -3y = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3y = 0 + 4
-3y = 0 + 4

Combine like terms: 0 + 4 = 4
-3y = 4

Divide each side by '-3'.
y = -1.333333333

Simplifying
y = -1.333333333

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 = {-1.333333333, 3.5}

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