(3r-7t)(2r+5t)=

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Solution for (3r-7t)(2r+5t)= equation: 


Simplifying
(3r + -7t)(2r + 5t) = 0

Multiply (3r + -7t) * (2r + 5t)
(3r * (2r + 5t) + -7t * (2r + 5t)) = 0
((2r * 3r + 5t * 3r) + -7t * (2r + 5t)) = 0

Reorder the terms:
((15rt + 6r2) + -7t * (2r + 5t)) = 0
((15rt + 6r2) + -7t * (2r + 5t)) = 0
(15rt + 6r2 + (2r * -7t + 5t * -7t)) = 0
(15rt + 6r2 + (-14rt + -35t2)) = 0

Reorder the terms:
(15rt + -14rt + 6r2 + -35t2) = 0

Combine like terms: 15rt + -14rt = 1rt
(1rt + 6r2 + -35t2) = 0

Solving
1rt + 6r2 + -35t2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3r + -7t)(2r + 5t) = 0


Subproblem 1
Set the factor '(3r + -7t)' equal to zero and attempt to solve:

Simplifying
3r + -7t = 0

Solving
3r + -7t = 0

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

Add '7t' to each side of the equation.
3r + -7t + 7t = 0 + 7t

Combine like terms: -7t + 7t = 0
3r + 0 = 0 + 7t
3r = 0 + 7t
Remove the zero:
3r = 7t

Divide each side by '3'.
r = 2.333333333t

Simplifying
r = 2.333333333t

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

Simplifying
2r + 5t = 0

Solving
2r + 5t = 0

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

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

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

Divide each side by '2'.
r = -2.5t

Simplifying
r = -2.5t
Solution
r = {2.333333333t, -2.5t}

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