3x-8x(2x+3)=-6(2x+5)

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Solution for 3x-8x(2x+3)=-6(2x+5) equation:


Simplifying
3x + -8x(2x + 3) = -6(2x + 5)

Reorder the terms:
3x + -8x(3 + 2x) = -6(2x + 5)
3x + (3 * -8x + 2x * -8x) = -6(2x + 5)
3x + (-24x + -16x2) = -6(2x + 5)

Combine like terms: 3x + -24x = -21x
-21x + -16x2 = -6(2x + 5)

Reorder the terms:
-21x + -16x2 = -6(5 + 2x)
-21x + -16x2 = (5 * -6 + 2x * -6)
-21x + -16x2 = (-30 + -12x)

Solving
-21x + -16x2 = -30 + -12x

Solving for variable 'x'.

Reorder the terms:
30 + -21x + 12x + -16x2 = -30 + -12x + 30 + 12x

Combine like terms: -21x + 12x = -9x
30 + -9x + -16x2 = -30 + -12x + 30 + 12x

Reorder the terms:
30 + -9x + -16x2 = -30 + 30 + -12x + 12x

Combine like terms: -30 + 30 = 0
30 + -9x + -16x2 = 0 + -12x + 12x
30 + -9x + -16x2 = -12x + 12x

Combine like terms: -12x + 12x = 0
30 + -9x + -16x2 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-1.875 + 0.5625x + x2 = 0

Move the constant term to the right:

Add '1.875' to each side of the equation.
-1.875 + 0.5625x + 1.875 + x2 = 0 + 1.875

Reorder the terms:
-1.875 + 1.875 + 0.5625x + x2 = 0 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + 0.5625x + x2 = 0 + 1.875
0.5625x + x2 = 0 + 1.875

Combine like terms: 0 + 1.875 = 1.875
0.5625x + x2 = 1.875

The x term is 0.5625x.  Take half its coefficient (0.28125).
Square it (0.0791015625) and add it to both sides.

Add '0.0791015625' to each side of the equation.
0.5625x + 0.0791015625 + x2 = 1.875 + 0.0791015625

Reorder the terms:
0.0791015625 + 0.5625x + x2 = 1.875 + 0.0791015625

Combine like terms: 1.875 + 0.0791015625 = 1.9541015625
0.0791015625 + 0.5625x + x2 = 1.9541015625

Factor a perfect square on the left side:
(x + 0.28125)(x + 0.28125) = 1.9541015625

Calculate the square root of the right side: 1.397891828

Break this problem into two subproblems by setting 
(x + 0.28125) equal to 1.397891828 and -1.397891828.

Subproblem 1

x + 0.28125 = 1.397891828 Simplifying x + 0.28125 = 1.397891828 Reorder the terms: 0.28125 + x = 1.397891828 Solving 0.28125 + x = 1.397891828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.28125' to each side of the equation. 0.28125 + -0.28125 + x = 1.397891828 + -0.28125 Combine like terms: 0.28125 + -0.28125 = 0.00000 0.00000 + x = 1.397891828 + -0.28125 x = 1.397891828 + -0.28125 Combine like terms: 1.397891828 + -0.28125 = 1.116641828 x = 1.116641828 Simplifying x = 1.116641828

Subproblem 2

x + 0.28125 = -1.397891828 Simplifying x + 0.28125 = -1.397891828 Reorder the terms: 0.28125 + x = -1.397891828 Solving 0.28125 + x = -1.397891828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.28125' to each side of the equation. 0.28125 + -0.28125 + x = -1.397891828 + -0.28125 Combine like terms: 0.28125 + -0.28125 = 0.00000 0.00000 + x = -1.397891828 + -0.28125 x = -1.397891828 + -0.28125 Combine like terms: -1.397891828 + -0.28125 = -1.679141828 x = -1.679141828 Simplifying x = -1.679141828

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.116641828, -1.679141828}

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