(10r+7)(3r-9)=0

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Solution for (10r+7)(3r-9)=0 equation: 


Simplifying
(10r + 7)(3r + -9) = 0

Reorder the terms:
(7 + 10r)(3r + -9) = 0

Reorder the terms:
(7 + 10r)(-9 + 3r) = 0

Multiply (7 + 10r) * (-9 + 3r)
(7(-9 + 3r) + 10r * (-9 + 3r)) = 0
((-9 * 7 + 3r * 7) + 10r * (-9 + 3r)) = 0
((-63 + 21r) + 10r * (-9 + 3r)) = 0
(-63 + 21r + (-9 * 10r + 3r * 10r)) = 0
(-63 + 21r + (-90r + 30r2)) = 0

Combine like terms: 21r + -90r = -69r
(-63 + -69r + 30r2) = 0

Solving
-63 + -69r + 30r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-21 + -23r + 10r2) = 0

Factor a trinomial.
3((-7 + -10r)(3 + -1r)) = 0

Ignore the factor 3.

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 '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1r = 0 + -3

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

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

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {-0.7, 3}

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