(x-4)(x-5)+(2x+3)(x-1)=x(2x-25-13)

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Solution for (x-4)(x-5)+(2x+3)(x-1)=x(2x-25-13) equation:


Simplifying
(x + -4)(x + -5) + (2x + 3)(x + -1) = x(2x + -25 + -13)

Reorder the terms:
(-4 + x)(x + -5) + (2x + 3)(x + -1) = x(2x + -25 + -13)

Reorder the terms:
(-4 + x)(-5 + x) + (2x + 3)(x + -1) = x(2x + -25 + -13)

Multiply (-4 + x) * (-5 + x)
(-4(-5 + x) + x(-5 + x)) + (2x + 3)(x + -1) = x(2x + -25 + -13)
((-5 * -4 + x * -4) + x(-5 + x)) + (2x + 3)(x + -1) = x(2x + -25 + -13)
((20 + -4x) + x(-5 + x)) + (2x + 3)(x + -1) = x(2x + -25 + -13)
(20 + -4x + (-5 * x + x * x)) + (2x + 3)(x + -1) = x(2x + -25 + -13)
(20 + -4x + (-5x + x2)) + (2x + 3)(x + -1) = x(2x + -25 + -13)

Combine like terms: -4x + -5x = -9x
(20 + -9x + x2) + (2x + 3)(x + -1) = x(2x + -25 + -13)

Reorder the terms:
20 + -9x + x2 + (3 + 2x)(x + -1) = x(2x + -25 + -13)

Reorder the terms:
20 + -9x + x2 + (3 + 2x)(-1 + x) = x(2x + -25 + -13)

Multiply (3 + 2x) * (-1 + x)
20 + -9x + x2 + (3(-1 + x) + 2x * (-1 + x)) = x(2x + -25 + -13)
20 + -9x + x2 + ((-1 * 3 + x * 3) + 2x * (-1 + x)) = x(2x + -25 + -13)
20 + -9x + x2 + ((-3 + 3x) + 2x * (-1 + x)) = x(2x + -25 + -13)
20 + -9x + x2 + (-3 + 3x + (-1 * 2x + x * 2x)) = x(2x + -25 + -13)
20 + -9x + x2 + (-3 + 3x + (-2x + 2x2)) = x(2x + -25 + -13)

Combine like terms: 3x + -2x = 1x
20 + -9x + x2 + (-3 + 1x + 2x2) = x(2x + -25 + -13)

Reorder the terms:
20 + -3 + -9x + 1x + x2 + 2x2 = x(2x + -25 + -13)

Combine like terms: 20 + -3 = 17
17 + -9x + 1x + x2 + 2x2 = x(2x + -25 + -13)

Combine like terms: -9x + 1x = -8x
17 + -8x + x2 + 2x2 = x(2x + -25 + -13)

Combine like terms: x2 + 2x2 = 3x2
17 + -8x + 3x2 = x(2x + -25 + -13)

Reorder the terms:
17 + -8x + 3x2 = x(-25 + -13 + 2x)

Combine like terms: -25 + -13 = -38
17 + -8x + 3x2 = x(-38 + 2x)
17 + -8x + 3x2 = (-38 * x + 2x * x)
17 + -8x + 3x2 = (-38x + 2x2)

Solving
17 + -8x + 3x2 = -38x + 2x2

Solving for variable 'x'.

Reorder the terms:
17 + -8x + 38x + 3x2 + -2x2 = -38x + 2x2 + 38x + -2x2

Combine like terms: -8x + 38x = 30x
17 + 30x + 3x2 + -2x2 = -38x + 2x2 + 38x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
17 + 30x + 1x2 = -38x + 2x2 + 38x + -2x2

Reorder the terms:
17 + 30x + 1x2 = -38x + 38x + 2x2 + -2x2

Combine like terms: -38x + 38x = 0
17 + 30x + 1x2 = 0 + 2x2 + -2x2
17 + 30x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
17 + 30x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + 30x + -17 + x2 = 0 + -17

Reorder the terms:
17 + -17 + 30x + x2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + 30x + x2 = 0 + -17
30x + x2 = 0 + -17

Combine like terms: 0 + -17 = -17
30x + x2 = -17

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = -17 + 225

Reorder the terms:
225 + 30x + x2 = -17 + 225

Combine like terms: -17 + 225 = 208
225 + 30x + x2 = 208

Factor a perfect square on the left side:
(x + 15)(x + 15) = 208

Calculate the square root of the right side: 14.422205102

Break this problem into two subproblems by setting 
(x + 15) equal to 14.422205102 and -14.422205102.

Subproblem 1

x + 15 = 14.422205102 Simplifying x + 15 = 14.422205102 Reorder the terms: 15 + x = 14.422205102 Solving 15 + x = 14.422205102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 14.422205102 + -15 Combine like terms: 15 + -15 = 0 0 + x = 14.422205102 + -15 x = 14.422205102 + -15 Combine like terms: 14.422205102 + -15 = -0.577794898 x = -0.577794898 Simplifying x = -0.577794898

Subproblem 2

x + 15 = -14.422205102 Simplifying x + 15 = -14.422205102 Reorder the terms: 15 + x = -14.422205102 Solving 15 + x = -14.422205102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -14.422205102 + -15 Combine like terms: 15 + -15 = 0 0 + x = -14.422205102 + -15 x = -14.422205102 + -15 Combine like terms: -14.422205102 + -15 = -29.422205102 x = -29.422205102 Simplifying x = -29.422205102

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.577794898, -29.422205102}

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