(10r+7)(3r-5)=0

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Solution for (10r+7)(3r-5)=0 equation: 


Simplifying
(10r + 7)(3r + -5) = 0

Reorder the terms:
(7 + 10r)(3r + -5) = 0

Reorder the terms:
(7 + 10r)(-5 + 3r) = 0

Multiply (7 + 10r) * (-5 + 3r)
(7(-5 + 3r) + 10r * (-5 + 3r)) = 0
((-5 * 7 + 3r * 7) + 10r * (-5 + 3r)) = 0
((-35 + 21r) + 10r * (-5 + 3r)) = 0
(-35 + 21r + (-5 * 10r + 3r * 10r)) = 0
(-35 + 21r + (-50r + 30r2)) = 0

Combine like terms: 21r + -50r = -29r
(-35 + -29r + 30r2) = 0

Solving
-35 + -29r + 30r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-7 + -10r)(5 + -3r) = 0


Subproblem 1
Set the factor '(-7 + -10r)' equal to zero and attempt to solve:

Simplifying
-7 + -10r = 0

Solving
-7 + -10r = 0

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

Add '7' to each side of the equation.
-7 + 7 + -10r = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -10r = 0 + 7
-10r = 0 + 7

Combine like terms: 0 + 7 = 7
-10r = 7

Divide each side by '-10'.
r = -0.7

Simplifying
r = -0.7

Subproblem 2
Set the factor '(5 + -3r)' equal to zero and attempt to solve:

Simplifying
5 + -3r = 0

Solving
5 + -3r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3r = 0 + -5
-3r = 0 + -5

Combine like terms: 0 + -5 = -5
-3r = -5

Divide each side by '-3'.
r = 1.666666667

Simplifying
r = 1.666666667
Solution
r = {-0.7, 1.666666667}

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