(x-1)(2x+3)=6

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Solution for (x-1)(2x+3)=6 equation:


Simplifying
(x + -1)(2x + 3) = 6

Reorder the terms:
(-1 + x)(2x + 3) = 6

Reorder the terms:
(-1 + x)(3 + 2x) = 6

Multiply (-1 + x) * (3 + 2x)
(-1(3 + 2x) + x(3 + 2x)) = 6
((3 * -1 + 2x * -1) + x(3 + 2x)) = 6
((-3 + -2x) + x(3 + 2x)) = 6
(-3 + -2x + (3 * x + 2x * x)) = 6
(-3 + -2x + (3x + 2x2)) = 6

Combine like terms: -2x + 3x = 1x
(-3 + 1x + 2x2) = 6

Solving
-3 + 1x + 2x2 = 6

Solving for variable 'x'.

Reorder the terms:
-3 + -6 + 1x + 2x2 = 6 + -6

Combine like terms: -3 + -6 = -9
-9 + 1x + 2x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-9 + 1x + 2x2 = 0

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

Divide each side by '2'.
-4.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + 0.5x + 4.5 + x2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + 0.5x + x2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + 0.5x + x2 = 0 + 4.5
0.5x + x2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
0.5x + x2 = 4.5

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 = 4.5 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 4.5 + 0.0625

Combine like terms: 4.5 + 0.0625 = 4.5625
0.0625 + 0.5x + x2 = 4.5625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(x + 0.25) equal to 2.136000936 and -2.136000936.

Subproblem 1

x + 0.25 = 2.136000936 Simplifying x + 0.25 = 2.136000936 Reorder the terms: 0.25 + x = 2.136000936 Solving 0.25 + x = 2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 2.136000936 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 2.136000936 + -0.25 x = 2.136000936 + -0.25 Combine like terms: 2.136000936 + -0.25 = 1.886000936 x = 1.886000936 Simplifying x = 1.886000936

Subproblem 2

x + 0.25 = -2.136000936 Simplifying x + 0.25 = -2.136000936 Reorder the terms: 0.25 + x = -2.136000936 Solving 0.25 + x = -2.136000936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -2.136000936 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -2.136000936 + -0.25 x = -2.136000936 + -0.25 Combine like terms: -2.136000936 + -0.25 = -2.386000936 x = -2.386000936 Simplifying x = -2.386000936

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.886000936, -2.386000936}

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