6(30r^2-r-132)=0

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Solution for 6(30r^2-r-132)=0 equation:


Simplifying
6(30r2 + -1r + -132) = 0

Reorder the terms:
6(-132 + -1r + 30r2) = 0
(-132 * 6 + -1r * 6 + 30r2 * 6) = 0
(-792 + -6r + 180r2) = 0

Solving
-792 + -6r + 180r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-132 + -1r + 30r2) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(-132 + -1r + 30r2)' equal to zero and attempt to solve: Simplifying -132 + -1r + 30r2 = 0 Solving -132 + -1r + 30r2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -4.4 + -0.03333333333r + r2 = 0.0 Move the constant term to the right: Add '4.4' to each side of the equation. -4.4 + -0.03333333333r + 4.4 + r2 = 0.0 + 4.4 Reorder the terms: -4.4 + 4.4 + -0.03333333333r + r2 = 0.0 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + -0.03333333333r + r2 = 0.0 + 4.4 -0.03333333333r + r2 = 0.0 + 4.4 Combine like terms: 0.0 + 4.4 = 4.4 -0.03333333333r + r2 = 4.4 The r term is -0.03333333333r. Take half its coefficient (-0.01666666667). Square it (0.0002777777779) and add it to both sides. Add '0.0002777777779' to each side of the equation. -0.03333333333r + 0.0002777777779 + r2 = 4.4 + 0.0002777777779 Reorder the terms: 0.0002777777779 + -0.03333333333r + r2 = 4.4 + 0.0002777777779 Combine like terms: 4.4 + 0.0002777777779 = 4.4002777777779 0.0002777777779 + -0.03333333333r + r2 = 4.4002777777779 Factor a perfect square on the left side: (r + -0.01666666667)(r + -0.01666666667) = 4.4002777777779 Calculate the square root of the right side: 2.097683908 Break this problem into two subproblems by setting (r + -0.01666666667) equal to 2.097683908 and -2.097683908.

Subproblem 1

r + -0.01666666667 = 2.097683908 Simplifying r + -0.01666666667 = 2.097683908 Reorder the terms: -0.01666666667 + r = 2.097683908 Solving -0.01666666667 + r = 2.097683908 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.01666666667' to each side of the equation. -0.01666666667 + 0.01666666667 + r = 2.097683908 + 0.01666666667 Combine like terms: -0.01666666667 + 0.01666666667 = 0.00000000000 0.00000000000 + r = 2.097683908 + 0.01666666667 r = 2.097683908 + 0.01666666667 Combine like terms: 2.097683908 + 0.01666666667 = 2.11435057467 r = 2.11435057467 Simplifying r = 2.11435057467

Subproblem 2

r + -0.01666666667 = -2.097683908 Simplifying r + -0.01666666667 = -2.097683908 Reorder the terms: -0.01666666667 + r = -2.097683908 Solving -0.01666666667 + r = -2.097683908 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.01666666667' to each side of the equation. -0.01666666667 + 0.01666666667 + r = -2.097683908 + 0.01666666667 Combine like terms: -0.01666666667 + 0.01666666667 = 0.00000000000 0.00000000000 + r = -2.097683908 + 0.01666666667 r = -2.097683908 + 0.01666666667 Combine like terms: -2.097683908 + 0.01666666667 = -2.08101724133 r = -2.08101724133 Simplifying r = -2.08101724133

Solution

The solution to the problem is based on the solutions from the subproblems. r = {2.11435057467, -2.08101724133}

Solution

r = {2.11435057467, -2.08101724133}

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