4x(3x-5)-(6+2)=x

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Solution for 4x(3x-5)-(6+2)=x equation:


Simplifying
4x(3x + -5) + -1(6 + 2) = x

Reorder the terms:
4x(-5 + 3x) + -1(6 + 2) = x
(-5 * 4x + 3x * 4x) + -1(6 + 2) = x
(-20x + 12x2) + -1(6 + 2) = x

Combine like terms: 6 + 2 = 8
-20x + 12x2 + -1(8) = x

Multiply -1 * 8
-20x + 12x2 + -8 = x

Reorder the terms:
-8 + -20x + 12x2 = x

Solving
-8 + -20x + 12x2 = x

Solving for variable 'x'.

Reorder the terms:
-8 + -20x + -1x + 12x2 = x + -1x

Combine like terms: -20x + -1x = -21x
-8 + -21x + 12x2 = x + -1x

Combine like terms: x + -1x = 0
-8 + -21x + 12x2 = 0

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

Divide each side by '12'.
-0.6666666667 + -1.75x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -1.75x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -1.75x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -1.75x + x2 = 0 + 0.6666666667
-1.75x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-1.75x + x2 = 0.6666666667

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = 0.6666666667 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = 0.6666666667 + 0.765625

Combine like terms: 0.6666666667 + 0.765625 = 1.4322916667
0.765625 + -1.75x + x2 = 1.4322916667

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = 1.4322916667

Calculate the square root of the right side: 1.196783885

Break this problem into two subproblems by setting 
(x + -0.875) equal to 1.196783885 and -1.196783885.

Subproblem 1

x + -0.875 = 1.196783885 Simplifying x + -0.875 = 1.196783885 Reorder the terms: -0.875 + x = 1.196783885 Solving -0.875 + x = 1.196783885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 1.196783885 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 1.196783885 + 0.875 x = 1.196783885 + 0.875 Combine like terms: 1.196783885 + 0.875 = 2.071783885 x = 2.071783885 Simplifying x = 2.071783885

Subproblem 2

x + -0.875 = -1.196783885 Simplifying x + -0.875 = -1.196783885 Reorder the terms: -0.875 + x = -1.196783885 Solving -0.875 + x = -1.196783885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -1.196783885 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -1.196783885 + 0.875 x = -1.196783885 + 0.875 Combine like terms: -1.196783885 + 0.875 = -0.321783885 x = -0.321783885 Simplifying x = -0.321783885

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.071783885, -0.321783885}

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