4(x+8)=3(x-9)x

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Solution for 4(x+8)=3(x-9)x equation:


Simplifying
4(x + 8) = 3(x + -9) * x

Reorder the terms:
4(8 + x) = 3(x + -9) * x
(8 * 4 + x * 4) = 3(x + -9) * x
(32 + 4x) = 3(x + -9) * x

Reorder the terms:
32 + 4x = 3(-9 + x) * x

Reorder the terms for easier multiplication:
32 + 4x = 3x(-9 + x)
32 + 4x = (-9 * 3x + x * 3x)
32 + 4x = (-27x + 3x2)

Solving
32 + 4x = -27x + 3x2

Solving for variable 'x'.

Combine like terms: 4x + 27x = 31x
32 + 31x + -3x2 = -27x + 3x2 + 27x + -3x2

Reorder the terms:
32 + 31x + -3x2 = -27x + 27x + 3x2 + -3x2

Combine like terms: -27x + 27x = 0
32 + 31x + -3x2 = 0 + 3x2 + -3x2
32 + 31x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
32 + 31x + -3x2 = 0

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

Divide each side by '-3'.
-10.66666667 + -10.33333333x + x2 = 0

Move the constant term to the right:

Add '10.66666667' to each side of the equation.
-10.66666667 + -10.33333333x + 10.66666667 + x2 = 0 + 10.66666667

Reorder the terms:
-10.66666667 + 10.66666667 + -10.33333333x + x2 = 0 + 10.66666667

Combine like terms: -10.66666667 + 10.66666667 = 0.00000000
0.00000000 + -10.33333333x + x2 = 0 + 10.66666667
-10.33333333x + x2 = 0 + 10.66666667

Combine like terms: 0 + 10.66666667 = 10.66666667
-10.33333333x + x2 = 10.66666667

The x term is -10.33333333x.  Take half its coefficient (-5.166666665).
Square it (26.69444443) and add it to both sides.

Add '26.69444443' to each side of the equation.
-10.33333333x + 26.69444443 + x2 = 10.66666667 + 26.69444443

Reorder the terms:
26.69444443 + -10.33333333x + x2 = 10.66666667 + 26.69444443

Combine like terms: 10.66666667 + 26.69444443 = 37.3611111
26.69444443 + -10.33333333x + x2 = 37.3611111

Factor a perfect square on the left side:
(x + -5.166666665)(x + -5.166666665) = 37.3611111

Calculate the square root of the right side: 6.112373606

Break this problem into two subproblems by setting 
(x + -5.166666665) equal to 6.112373606 and -6.112373606.

Subproblem 1

x + -5.166666665 = 6.112373606 Simplifying x + -5.166666665 = 6.112373606 Reorder the terms: -5.166666665 + x = 6.112373606 Solving -5.166666665 + x = 6.112373606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.166666665' to each side of the equation. -5.166666665 + 5.166666665 + x = 6.112373606 + 5.166666665 Combine like terms: -5.166666665 + 5.166666665 = 0.000000000 0.000000000 + x = 6.112373606 + 5.166666665 x = 6.112373606 + 5.166666665 Combine like terms: 6.112373606 + 5.166666665 = 11.279040271 x = 11.279040271 Simplifying x = 11.279040271

Subproblem 2

x + -5.166666665 = -6.112373606 Simplifying x + -5.166666665 = -6.112373606 Reorder the terms: -5.166666665 + x = -6.112373606 Solving -5.166666665 + x = -6.112373606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.166666665' to each side of the equation. -5.166666665 + 5.166666665 + x = -6.112373606 + 5.166666665 Combine like terms: -5.166666665 + 5.166666665 = 0.000000000 0.000000000 + x = -6.112373606 + 5.166666665 x = -6.112373606 + 5.166666665 Combine like terms: -6.112373606 + 5.166666665 = -0.945706941 x = -0.945706941 Simplifying x = -0.945706941

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.279040271, -0.945706941}

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