3x(x-6)=-4

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


Simplifying
3x(x + -6) = -4

Reorder the terms:
3x(-6 + x) = -4
(-6 * 3x + x * 3x) = -4
(-18x + 3x2) = -4

Solving
-18x + 3x2 = -4

Solving for variable 'x'.

Reorder the terms:
4 + -18x + 3x2 = -4 + 4

Combine like terms: -4 + 4 = 0
4 + -18x + 3x2 = 0

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

Divide each side by '3'.
1.333333333 + -6x + x2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -6x + -1.333333333 + x2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -6x + x2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -6x + x2 = 0 + -1.333333333
-6x + x2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-6x + x2 = -1.333333333

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -1.333333333 + 9

Reorder the terms:
9 + -6x + x2 = -1.333333333 + 9

Combine like terms: -1.333333333 + 9 = 7.666666667
9 + -6x + x2 = 7.666666667

Factor a perfect square on the left side:
(x + -3)(x + -3) = 7.666666667

Calculate the square root of the right side: 2.768874621

Break this problem into two subproblems by setting 
(x + -3) equal to 2.768874621 and -2.768874621.

Subproblem 1

x + -3 = 2.768874621 Simplifying x + -3 = 2.768874621 Reorder the terms: -3 + x = 2.768874621 Solving -3 + x = 2.768874621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.768874621 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.768874621 + 3 x = 2.768874621 + 3 Combine like terms: 2.768874621 + 3 = 5.768874621 x = 5.768874621 Simplifying x = 5.768874621

Subproblem 2

x + -3 = -2.768874621 Simplifying x + -3 = -2.768874621 Reorder the terms: -3 + x = -2.768874621 Solving -3 + x = -2.768874621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.768874621 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.768874621 + 3 x = -2.768874621 + 3 Combine like terms: -2.768874621 + 3 = 0.231125379 x = 0.231125379 Simplifying x = 0.231125379

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.768874621, 0.231125379}

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