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

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


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

Reorder the terms:
(4 + x)(x + -6) = 4x

Reorder the terms:
(4 + x)(-6 + x) = 4x

Multiply (4 + x) * (-6 + x)
(4(-6 + x) + x(-6 + x)) = 4x
((-6 * 4 + x * 4) + x(-6 + x)) = 4x
((-24 + 4x) + x(-6 + x)) = 4x
(-24 + 4x + (-6 * x + x * x)) = 4x
(-24 + 4x + (-6x + x2)) = 4x

Combine like terms: 4x + -6x = -2x
(-24 + -2x + x2) = 4x

Solving
-24 + -2x + x2 = 4x

Solving for variable 'x'.

Reorder the terms:
-24 + -2x + -4x + x2 = 4x + -4x

Combine like terms: -2x + -4x = -6x
-24 + -6x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-24 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -6x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + -6x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -6x + x2 = 0 + 24
-6x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
-6x + x2 = 24

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 = 24 + 9

Reorder the terms:
9 + -6x + x2 = 24 + 9

Combine like terms: 24 + 9 = 33
9 + -6x + x2 = 33

Factor a perfect square on the left side:
(x + -3)(x + -3) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(x + -3) equal to 5.744562647 and -5.744562647.

Subproblem 1

x + -3 = 5.744562647 Simplifying x + -3 = 5.744562647 Reorder the terms: -3 + x = 5.744562647 Solving -3 + x = 5.744562647 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 = 5.744562647 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.744562647 + 3 x = 5.744562647 + 3 Combine like terms: 5.744562647 + 3 = 8.744562647 x = 8.744562647 Simplifying x = 8.744562647

Subproblem 2

x + -3 = -5.744562647 Simplifying x + -3 = -5.744562647 Reorder the terms: -3 + x = -5.744562647 Solving -3 + x = -5.744562647 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 = -5.744562647 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.744562647 + 3 x = -5.744562647 + 3 Combine like terms: -5.744562647 + 3 = -2.744562647 x = -2.744562647 Simplifying x = -2.744562647

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.744562647, -2.744562647}

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