(12r+7)(5r-15)=0

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Solution for (12r+7)(5r-15)=0 equation: 


Simplifying
(12r + 7)(5r + -15) = 0

Reorder the terms:
(7 + 12r)(5r + -15) = 0

Reorder the terms:
(7 + 12r)(-15 + 5r) = 0

Multiply (7 + 12r) * (-15 + 5r)
(7(-15 + 5r) + 12r * (-15 + 5r)) = 0
((-15 * 7 + 5r * 7) + 12r * (-15 + 5r)) = 0
((-105 + 35r) + 12r * (-15 + 5r)) = 0
(-105 + 35r + (-15 * 12r + 5r * 12r)) = 0
(-105 + 35r + (-180r + 60r2)) = 0

Combine like terms: 35r + -180r = -145r
(-105 + -145r + 60r2) = 0

Solving
-105 + -145r + 60r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-21 + -29r + 12r2) = 0

Factor a trinomial.
5((-7 + -12r)(3 + -1r)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-7 + -12r)' equal to zero and attempt to solve:

Simplifying
-7 + -12r = 0

Solving
-7 + -12r = 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 + -12r = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -12r = 0 + 7
-12r = 0 + 7

Combine like terms: 0 + 7 = 7
-12r = 7

Divide each side by '-12'.
r = -0.5833333333

Simplifying
r = -0.5833333333

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 = {-0.5833333333, 3}

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