6x(-x)=3x+8

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Solution for 6x(-x)=3x+8 equation:


Simplifying
6x(-1x) = 3x + 8

Remove parenthesis around (-1x)
6x * -1x = 3x + 8

Reorder the terms for easier multiplication:
6 * -1x * x = 3x + 8

Multiply 6 * -1
-6x * x = 3x + 8

Multiply x * x
-6x2 = 3x + 8

Reorder the terms:
-6x2 = 8 + 3x

Solving
-6x2 = 8 + 3x

Solving for variable 'x'.

Reorder the terms:
-8 + -3x + -6x2 = 8 + 3x + -8 + -3x

Reorder the terms:
-8 + -3x + -6x2 = 8 + -8 + 3x + -3x

Combine like terms: 8 + -8 = 0
-8 + -3x + -6x2 = 0 + 3x + -3x
-8 + -3x + -6x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-8 + -3x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 3x + 6x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(8 + 3x + 6x2)' equal to zero and attempt to solve: Simplifying 8 + 3x + 6x2 = 0 Solving 8 + 3x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.333333333 + 0.5x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 0.5x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 0.5x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 0.5x + x2 = 0 + -1.333333333 0.5x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 0.5x + x2 = -1.333333333 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = -1.333333333 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = -1.333333333 + 0.0625 Combine like terms: -1.333333333 + 0.0625 = -1.270833333 0.0625 + 0.5x + x2 = -1.270833333 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = -1.270833333 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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