8(5x-x)-3x(5x-x)=3x(x-6)-4(x-6)-13

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Solution for 8(5x-x)-3x(5x-x)=3x(x-6)-4(x-6)-13 equation:


Simplifying
8(5x + -1x) + -3x(5x + -1x) = 3x(x + -6) + -4(x + -6) + -13

Combine like terms: 5x + -1x = 4x
8(4x) + -3x(5x + -1x) = 3x(x + -6) + -4(x + -6) + -13

Remove parenthesis around (4x)
8 * 4x + -3x(5x + -1x) = 3x(x + -6) + -4(x + -6) + -13

Multiply 8 * 4
32x + -3x(5x + -1x) = 3x(x + -6) + -4(x + -6) + -13

Combine like terms: 5x + -1x = 4x
32x + -3x(4x) = 3x(x + -6) + -4(x + -6) + -13

Remove parenthesis around (4x)
32x + -3x * 4x = 3x(x + -6) + -4(x + -6) + -13

Reorder the terms for easier multiplication:
32x + -3 * 4x * x = 3x(x + -6) + -4(x + -6) + -13

Multiply -3 * 4
32x + -12x * x = 3x(x + -6) + -4(x + -6) + -13

Multiply x * x
32x + -12x2 = 3x(x + -6) + -4(x + -6) + -13

Reorder the terms:
32x + -12x2 = 3x(-6 + x) + -4(x + -6) + -13
32x + -12x2 = (-6 * 3x + x * 3x) + -4(x + -6) + -13
32x + -12x2 = (-18x + 3x2) + -4(x + -6) + -13

Reorder the terms:
32x + -12x2 = -18x + 3x2 + -4(-6 + x) + -13
32x + -12x2 = -18x + 3x2 + (-6 * -4 + x * -4) + -13
32x + -12x2 = -18x + 3x2 + (24 + -4x) + -13

Reorder the terms:
32x + -12x2 = 24 + -13 + -18x + -4x + 3x2

Combine like terms: 24 + -13 = 11
32x + -12x2 = 11 + -18x + -4x + 3x2

Combine like terms: -18x + -4x = -22x
32x + -12x2 = 11 + -22x + 3x2

Solving
32x + -12x2 = 11 + -22x + 3x2

Solving for variable 'x'.

Reorder the terms:
-11 + 32x + 22x + -12x2 + -3x2 = 11 + -22x + 3x2 + -11 + 22x + -3x2

Combine like terms: 32x + 22x = 54x
-11 + 54x + -12x2 + -3x2 = 11 + -22x + 3x2 + -11 + 22x + -3x2

Combine like terms: -12x2 + -3x2 = -15x2
-11 + 54x + -15x2 = 11 + -22x + 3x2 + -11 + 22x + -3x2

Reorder the terms:
-11 + 54x + -15x2 = 11 + -11 + -22x + 22x + 3x2 + -3x2

Combine like terms: 11 + -11 = 0
-11 + 54x + -15x2 = 0 + -22x + 22x + 3x2 + -3x2
-11 + 54x + -15x2 = -22x + 22x + 3x2 + -3x2

Combine like terms: -22x + 22x = 0
-11 + 54x + -15x2 = 0 + 3x2 + -3x2
-11 + 54x + -15x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-11 + 54x + -15x2 = 0

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
0.7333333333 + -3.6x + x2 = 0

Move the constant term to the right:

Add '-0.7333333333' to each side of the equation.
0.7333333333 + -3.6x + -0.7333333333 + x2 = 0 + -0.7333333333

Reorder the terms:
0.7333333333 + -0.7333333333 + -3.6x + x2 = 0 + -0.7333333333

Combine like terms: 0.7333333333 + -0.7333333333 = 0.0000000000
0.0000000000 + -3.6x + x2 = 0 + -0.7333333333
-3.6x + x2 = 0 + -0.7333333333

Combine like terms: 0 + -0.7333333333 = -0.7333333333
-3.6x + x2 = -0.7333333333

The x term is -3.6x.  Take half its coefficient (-1.8).
Square it (3.24) and add it to both sides.

Add '3.24' to each side of the equation.
-3.6x + 3.24 + x2 = -0.7333333333 + 3.24

Reorder the terms:
3.24 + -3.6x + x2 = -0.7333333333 + 3.24

Combine like terms: -0.7333333333 + 3.24 = 2.5066666667
3.24 + -3.6x + x2 = 2.5066666667

Factor a perfect square on the left side:
(x + -1.8)(x + -1.8) = 2.5066666667

Calculate the square root of the right side: 1.583245612

Break this problem into two subproblems by setting 
(x + -1.8) equal to 1.583245612 and -1.583245612.

Subproblem 1

x + -1.8 = 1.583245612 Simplifying x + -1.8 = 1.583245612 Reorder the terms: -1.8 + x = 1.583245612 Solving -1.8 + x = 1.583245612 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 1.583245612 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 1.583245612 + 1.8 x = 1.583245612 + 1.8 Combine like terms: 1.583245612 + 1.8 = 3.383245612 x = 3.383245612 Simplifying x = 3.383245612

Subproblem 2

x + -1.8 = -1.583245612 Simplifying x + -1.8 = -1.583245612 Reorder the terms: -1.8 + x = -1.583245612 Solving -1.8 + x = -1.583245612 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -1.583245612 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -1.583245612 + 1.8 x = -1.583245612 + 1.8 Combine like terms: -1.583245612 + 1.8 = 0.216754388 x = 0.216754388 Simplifying x = 0.216754388

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.383245612, 0.216754388}

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