-6b(-5+2b)+4(6b+8)=

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Solution for -6b(-5+2b)+4(6b+8)= equation:


Simplifying
-6b(-5 + 2b) + 4(6b + 8) = 0
(-5 * -6b + 2b * -6b) + 4(6b + 8) = 0
(30b + -12b2) + 4(6b + 8) = 0

Reorder the terms:
30b + -12b2 + 4(8 + 6b) = 0
30b + -12b2 + (8 * 4 + 6b * 4) = 0
30b + -12b2 + (32 + 24b) = 0

Reorder the terms:
32 + 30b + 24b + -12b2 = 0

Combine like terms: 30b + 24b = 54b
32 + 54b + -12b2 = 0

Solving
32 + 54b + -12b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + 27b + -6b2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(16 + 27b + -6b2)' equal to zero and attempt to solve: Simplifying 16 + 27b + -6b2 = 0 Solving 16 + 27b + -6b2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -2.666666667 + -4.5b + b2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + -4.5b + 2.666666667 + b2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + -4.5b + b2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + -4.5b + b2 = 0 + 2.666666667 -4.5b + b2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 -4.5b + b2 = 2.666666667 The b term is -4.5b. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5b + 5.0625 + b2 = 2.666666667 + 5.0625 Reorder the terms: 5.0625 + -4.5b + b2 = 2.666666667 + 5.0625 Combine like terms: 2.666666667 + 5.0625 = 7.729166667 5.0625 + -4.5b + b2 = 7.729166667 Factor a perfect square on the left side: (b + -2.25)(b + -2.25) = 7.729166667 Calculate the square root of the right side: 2.780137886 Break this problem into two subproblems by setting (b + -2.25) equal to 2.780137886 and -2.780137886.

Subproblem 1

b + -2.25 = 2.780137886 Simplifying b + -2.25 = 2.780137886 Reorder the terms: -2.25 + b = 2.780137886 Solving -2.25 + b = 2.780137886 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + b = 2.780137886 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + b = 2.780137886 + 2.25 b = 2.780137886 + 2.25 Combine like terms: 2.780137886 + 2.25 = 5.030137886 b = 5.030137886 Simplifying b = 5.030137886

Subproblem 2

b + -2.25 = -2.780137886 Simplifying b + -2.25 = -2.780137886 Reorder the terms: -2.25 + b = -2.780137886 Solving -2.25 + b = -2.780137886 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + b = -2.780137886 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + b = -2.780137886 + 2.25 b = -2.780137886 + 2.25 Combine like terms: -2.780137886 + 2.25 = -0.530137886 b = -0.530137886 Simplifying b = -0.530137886

Solution

The solution to the problem is based on the solutions from the subproblems. b = {5.030137886, -0.530137886}

Solution

b = {5.030137886, -0.530137886}

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