1q+2=(-6q-3)(8q+4)

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Solution for 1q+2=(-6q-3)(8q+4) equation:


Simplifying
1q + 2 = (-6q + -3)(8q + 4)

Reorder the terms:
2 + 1q = (-6q + -3)(8q + 4)

Reorder the terms:
2 + 1q = (-3 + -6q)(8q + 4)

Reorder the terms:
2 + 1q = (-3 + -6q)(4 + 8q)

Multiply (-3 + -6q) * (4 + 8q)
2 + 1q = (-3(4 + 8q) + -6q * (4 + 8q))
2 + 1q = ((4 * -3 + 8q * -3) + -6q * (4 + 8q))
2 + 1q = ((-12 + -24q) + -6q * (4 + 8q))
2 + 1q = (-12 + -24q + (4 * -6q + 8q * -6q))
2 + 1q = (-12 + -24q + (-24q + -48q2))

Combine like terms: -24q + -24q = -48q
2 + 1q = (-12 + -48q + -48q2)

Solving
2 + 1q = -12 + -48q + -48q2

Solving for variable 'q'.

Reorder the terms:
2 + 12 + 1q + 48q + 48q2 = -12 + -48q + -48q2 + 12 + 48q + 48q2

Combine like terms: 2 + 12 = 14
14 + 1q + 48q + 48q2 = -12 + -48q + -48q2 + 12 + 48q + 48q2

Combine like terms: 1q + 48q = 49q
14 + 49q + 48q2 = -12 + -48q + -48q2 + 12 + 48q + 48q2

Reorder the terms:
14 + 49q + 48q2 = -12 + 12 + -48q + 48q + -48q2 + 48q2

Combine like terms: -12 + 12 = 0
14 + 49q + 48q2 = 0 + -48q + 48q + -48q2 + 48q2
14 + 49q + 48q2 = -48q + 48q + -48q2 + 48q2

Combine like terms: -48q + 48q = 0
14 + 49q + 48q2 = 0 + -48q2 + 48q2
14 + 49q + 48q2 = -48q2 + 48q2

Combine like terms: -48q2 + 48q2 = 0
14 + 49q + 48q2 = 0

Begin completing the square.  Divide all terms by
48 the coefficient of the squared term: 

Divide each side by '48'.
0.2916666667 + 1.020833333q + q2 = 0

Move the constant term to the right:

Add '-0.2916666667' to each side of the equation.
0.2916666667 + 1.020833333q + -0.2916666667 + q2 = 0 + -0.2916666667

Reorder the terms:
0.2916666667 + -0.2916666667 + 1.020833333q + q2 = 0 + -0.2916666667

Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000
0.0000000000 + 1.020833333q + q2 = 0 + -0.2916666667
1.020833333q + q2 = 0 + -0.2916666667

Combine like terms: 0 + -0.2916666667 = -0.2916666667
1.020833333q + q2 = -0.2916666667

The q term is 1.020833333q.  Take half its coefficient (0.5104166665).
Square it (0.2605251734) and add it to both sides.

Add '0.2605251734' to each side of the equation.
1.020833333q + 0.2605251734 + q2 = -0.2916666667 + 0.2605251734

Reorder the terms:
0.2605251734 + 1.020833333q + q2 = -0.2916666667 + 0.2605251734

Combine like terms: -0.2916666667 + 0.2605251734 = -0.0311414933
0.2605251734 + 1.020833333q + q2 = -0.0311414933

Factor a perfect square on the left side:
(q + 0.5104166665)(q + 0.5104166665) = -0.0311414933

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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