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

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


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

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

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

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

Combine like terms: 5x + -8x = -3x
(-20 + -3x + 2x2) = x(x + -6)

Reorder the terms:
-20 + -3x + 2x2 = x(-6 + x)
-20 + -3x + 2x2 = (-6 * x + x * x)
-20 + -3x + 2x2 = (-6x + x2)

Solving
-20 + -3x + 2x2 = -6x + x2

Solving for variable 'x'.

Reorder the terms:
-20 + -3x + 6x + 2x2 + -1x2 = -6x + x2 + 6x + -1x2

Combine like terms: -3x + 6x = 3x
-20 + 3x + 2x2 + -1x2 = -6x + x2 + 6x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-20 + 3x + 1x2 = -6x + x2 + 6x + -1x2

Reorder the terms:
-20 + 3x + 1x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
-20 + 3x + 1x2 = 0 + x2 + -1x2
-20 + 3x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-20 + 3x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 3x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 3x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 3x + x2 = 0 + 20
3x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
3x + x2 = 20

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 20 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 20 + 2.25

Combine like terms: 20 + 2.25 = 22.25
2.25 + 3x + x2 = 22.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(x + 1.5) equal to 4.716990566 and -4.716990566.

Subproblem 1

x + 1.5 = 4.716990566 Simplifying x + 1.5 = 4.716990566 Reorder the terms: 1.5 + x = 4.716990566 Solving 1.5 + x = 4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 4.716990566 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 4.716990566 + -1.5 x = 4.716990566 + -1.5 Combine like terms: 4.716990566 + -1.5 = 3.216990566 x = 3.216990566 Simplifying x = 3.216990566

Subproblem 2

x + 1.5 = -4.716990566 Simplifying x + 1.5 = -4.716990566 Reorder the terms: 1.5 + x = -4.716990566 Solving 1.5 + x = -4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -4.716990566 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -4.716990566 + -1.5 x = -4.716990566 + -1.5 Combine like terms: -4.716990566 + -1.5 = -6.216990566 x = -6.216990566 Simplifying x = -6.216990566

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.216990566, -6.216990566}

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