(6x+2)(x-5)=8

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


Simplifying
(6x + 2)(x + -5) = 8

Reorder the terms:
(2 + 6x)(x + -5) = 8

Reorder the terms:
(2 + 6x)(-5 + x) = 8

Multiply (2 + 6x) * (-5 + x)
(2(-5 + x) + 6x * (-5 + x)) = 8
((-5 * 2 + x * 2) + 6x * (-5 + x)) = 8
((-10 + 2x) + 6x * (-5 + x)) = 8
(-10 + 2x + (-5 * 6x + x * 6x)) = 8
(-10 + 2x + (-30x + 6x2)) = 8

Combine like terms: 2x + -30x = -28x
(-10 + -28x + 6x2) = 8

Solving
-10 + -28x + 6x2 = 8

Solving for variable 'x'.

Reorder the terms:
-10 + -8 + -28x + 6x2 = 8 + -8

Combine like terms: -10 + -8 = -18
-18 + -28x + 6x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-18 + -28x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -14x + 3x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-9 + -14x + 3x2)' equal to zero and attempt to solve: Simplifying -9 + -14x + 3x2 = 0 Solving -9 + -14x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + -4.666666667x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -4.666666667x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -4.666666667x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4.666666667x + x2 = 0 + 3 -4.666666667x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -4.666666667x + x2 = 3 The x term is -4.666666667x. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667x + 5.444444448 + x2 = 3 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667x + x2 = 3 + 5.444444448 Combine like terms: 3 + 5.444444448 = 8.444444448 5.444444448 + -4.666666667x + x2 = 8.444444448 Factor a perfect square on the left side: (x + -2.333333334)(x + -2.333333334) = 8.444444448 Calculate the square root of the right side: 2.90593263 Break this problem into two subproblems by setting (x + -2.333333334) equal to 2.90593263 and -2.90593263.

Subproblem 1

x + -2.333333334 = 2.90593263 Simplifying x + -2.333333334 = 2.90593263 Reorder the terms: -2.333333334 + x = 2.90593263 Solving -2.333333334 + x = 2.90593263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = 2.90593263 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 2.90593263 + 2.333333334 x = 2.90593263 + 2.333333334 Combine like terms: 2.90593263 + 2.333333334 = 5.239265964 x = 5.239265964 Simplifying x = 5.239265964

Subproblem 2

x + -2.333333334 = -2.90593263 Simplifying x + -2.333333334 = -2.90593263 Reorder the terms: -2.333333334 + x = -2.90593263 Solving -2.333333334 + x = -2.90593263 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = -2.90593263 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -2.90593263 + 2.333333334 x = -2.90593263 + 2.333333334 Combine like terms: -2.90593263 + 2.333333334 = -0.572599296 x = -0.572599296 Simplifying x = -0.572599296

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.239265964, -0.572599296}

Solution

x = {5.239265964, -0.572599296}

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