(6r-4)*(6r-5)=

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Solution for (6r-4)*(6r-5)= equation: 


Simplifying
(6r + -4)(6r + -5) = 0

Reorder the terms:
(-4 + 6r)(6r + -5) = 0

Reorder the terms:
(-4 + 6r)(-5 + 6r) = 0

Multiply (-4 + 6r) * (-5 + 6r)
(-4(-5 + 6r) + 6r * (-5 + 6r)) = 0
((-5 * -4 + 6r * -4) + 6r * (-5 + 6r)) = 0
((20 + -24r) + 6r * (-5 + 6r)) = 0
(20 + -24r + (-5 * 6r + 6r * 6r)) = 0
(20 + -24r + (-30r + 36r2)) = 0

Combine like terms: -24r + -30r = -54r
(20 + -54r + 36r2) = 0

Solving
20 + -54r + 36r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -27r + 18r2) = 0

Factor a trinomial.
2((2 + -3r)(5 + -6r)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2 + -3r)' equal to zero and attempt to solve:

Simplifying
2 + -3r = 0

Solving
2 + -3r = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3r = 0 + -2
-3r = 0 + -2

Combine like terms: 0 + -2 = -2
-3r = -2

Divide each side by '-3'.
r = 0.6666666667

Simplifying
r = 0.6666666667

Subproblem 2
Set the factor '(5 + -6r)' equal to zero and attempt to solve:

Simplifying
5 + -6r = 0

Solving
5 + -6r = 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 + -6r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6r = 0 + -5
-6r = 0 + -5

Combine like terms: 0 + -5 = -5
-6r = -5

Divide each side by '-6'.
r = 0.8333333333

Simplifying
r = 0.8333333333
Solution
r = {0.6666666667, 0.8333333333}

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