(7y-4t)(2y+5t)=

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Solution for (7y-4t)(2y+5t)= equation: 


Simplifying
(7y + -4t)(2y + 5t) = 0

Reorder the terms:
(-4t + 7y)(2y + 5t) = 0

Reorder the terms:
(-4t + 7y)(5t + 2y) = 0

Multiply (-4t + 7y) * (5t + 2y)
(-4t * (5t + 2y) + 7y * (5t + 2y)) = 0
((5t * -4t + 2y * -4t) + 7y * (5t + 2y)) = 0

Reorder the terms:
((-8ty + -20t2) + 7y * (5t + 2y)) = 0
((-8ty + -20t2) + 7y * (5t + 2y)) = 0
(-8ty + -20t2 + (5t * 7y + 2y * 7y)) = 0
(-8ty + -20t2 + (35ty + 14y2)) = 0

Reorder the terms:
(-8ty + 35ty + -20t2 + 14y2) = 0

Combine like terms: -8ty + 35ty = 27ty
(27ty + -20t2 + 14y2) = 0

Solving
27ty + -20t2 + 14y2 = 0

Solving for variable 't'.

Factor a trinomial.
(-5t + -2y)(4t + -7y) = 0


Subproblem 1
Set the factor '(-5t + -2y)' equal to zero and attempt to solve:

Simplifying
-5t + -2y = 0

Solving
-5t + -2y = 0

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

Add '2y' to each side of the equation.
-5t + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
-5t + 0 = 0 + 2y
-5t = 0 + 2y
Remove the zero:
-5t = 2y

Divide each side by '-5'.
t = -0.4y

Simplifying
t = -0.4y

Subproblem 2
Set the factor '(4t + -7y)' equal to zero and attempt to solve:

Simplifying
4t + -7y = 0

Solving
4t + -7y = 0

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

Add '7y' to each side of the equation.
4t + -7y + 7y = 0 + 7y

Combine like terms: -7y + 7y = 0
4t + 0 = 0 + 7y
4t = 0 + 7y
Remove the zero:
4t = 7y

Divide each side by '4'.
t = 1.75y

Simplifying
t = 1.75y
Solution
t = {-0.4y, 1.75y}

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