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

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


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

Reorder the terms:
(-5 + 2x)(x + -4) = 6(x + 4)

Reorder the terms:
(-5 + 2x)(-4 + x) = 6(x + 4)

Multiply (-5 + 2x) * (-4 + x)
(-5(-4 + x) + 2x * (-4 + x)) = 6(x + 4)
((-4 * -5 + x * -5) + 2x * (-4 + x)) = 6(x + 4)
((20 + -5x) + 2x * (-4 + x)) = 6(x + 4)
(20 + -5x + (-4 * 2x + x * 2x)) = 6(x + 4)
(20 + -5x + (-8x + 2x2)) = 6(x + 4)

Combine like terms: -5x + -8x = -13x
(20 + -13x + 2x2) = 6(x + 4)

Reorder the terms:
20 + -13x + 2x2 = 6(4 + x)
20 + -13x + 2x2 = (4 * 6 + x * 6)
20 + -13x + 2x2 = (24 + 6x)

Solving
20 + -13x + 2x2 = 24 + 6x

Solving for variable 'x'.

Reorder the terms:
20 + -24 + -13x + -6x + 2x2 = 24 + 6x + -24 + -6x

Combine like terms: 20 + -24 = -4
-4 + -13x + -6x + 2x2 = 24 + 6x + -24 + -6x

Combine like terms: -13x + -6x = -19x
-4 + -19x + 2x2 = 24 + 6x + -24 + -6x

Reorder the terms:
-4 + -19x + 2x2 = 24 + -24 + 6x + -6x

Combine like terms: 24 + -24 = 0
-4 + -19x + 2x2 = 0 + 6x + -6x
-4 + -19x + 2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-4 + -19x + 2x2 = 0

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

Divide each side by '2'.
-2 + -9.5x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -9.5x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -9.5x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -9.5x + x2 = 0 + 2
-9.5x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-9.5x + x2 = 2

The x term is -9.5x.  Take half its coefficient (-4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
-9.5x + 22.5625 + x2 = 2 + 22.5625

Reorder the terms:
22.5625 + -9.5x + x2 = 2 + 22.5625

Combine like terms: 2 + 22.5625 = 24.5625
22.5625 + -9.5x + x2 = 24.5625

Factor a perfect square on the left side:
(x + -4.75)(x + -4.75) = 24.5625

Calculate the square root of the right side: 4.9560569

Break this problem into two subproblems by setting 
(x + -4.75) equal to 4.9560569 and -4.9560569.

Subproblem 1

x + -4.75 = 4.9560569 Simplifying x + -4.75 = 4.9560569 Reorder the terms: -4.75 + x = 4.9560569 Solving -4.75 + x = 4.9560569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 4.9560569 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 4.9560569 + 4.75 x = 4.9560569 + 4.75 Combine like terms: 4.9560569 + 4.75 = 9.7060569 x = 9.7060569 Simplifying x = 9.7060569

Subproblem 2

x + -4.75 = -4.9560569 Simplifying x + -4.75 = -4.9560569 Reorder the terms: -4.75 + x = -4.9560569 Solving -4.75 + x = -4.9560569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -4.9560569 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -4.9560569 + 4.75 x = -4.9560569 + 4.75 Combine like terms: -4.9560569 + 4.75 = -0.2060569 x = -0.2060569 Simplifying x = -0.2060569

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.7060569, -0.2060569}

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