(3x+2)(-x+5)=x-7

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Solution for (3x+2)(-x+5)=x-7 equation:


Simplifying
(3x + 2)(-1x + 5) = x + -7

Reorder the terms:
(2 + 3x)(-1x + 5) = x + -7

Reorder the terms:
(2 + 3x)(5 + -1x) = x + -7

Multiply (2 + 3x) * (5 + -1x)
(2(5 + -1x) + 3x * (5 + -1x)) = x + -7
((5 * 2 + -1x * 2) + 3x * (5 + -1x)) = x + -7
((10 + -2x) + 3x * (5 + -1x)) = x + -7
(10 + -2x + (5 * 3x + -1x * 3x)) = x + -7
(10 + -2x + (15x + -3x2)) = x + -7

Combine like terms: -2x + 15x = 13x
(10 + 13x + -3x2) = x + -7

Reorder the terms:
10 + 13x + -3x2 = -7 + x

Solving
10 + 13x + -3x2 = -7 + x

Solving for variable 'x'.

Reorder the terms:
10 + 7 + 13x + -1x + -3x2 = -7 + x + 7 + -1x

Combine like terms: 10 + 7 = 17
17 + 13x + -1x + -3x2 = -7 + x + 7 + -1x

Combine like terms: 13x + -1x = 12x
17 + 12x + -3x2 = -7 + x + 7 + -1x

Reorder the terms:
17 + 12x + -3x2 = -7 + 7 + x + -1x

Combine like terms: -7 + 7 = 0
17 + 12x + -3x2 = 0 + x + -1x
17 + 12x + -3x2 = x + -1x

Combine like terms: x + -1x = 0
17 + 12x + -3x2 = 0

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

Divide each side by '-3'.
-5.666666667 + -4x + x2 = 0

Move the constant term to the right:

Add '5.666666667' to each side of the equation.
-5.666666667 + -4x + 5.666666667 + x2 = 0 + 5.666666667

Reorder the terms:
-5.666666667 + 5.666666667 + -4x + x2 = 0 + 5.666666667

Combine like terms: -5.666666667 + 5.666666667 = 0.000000000
0.000000000 + -4x + x2 = 0 + 5.666666667
-4x + x2 = 0 + 5.666666667

Combine like terms: 0 + 5.666666667 = 5.666666667
-4x + x2 = 5.666666667

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 5.666666667 + 4

Reorder the terms:
4 + -4x + x2 = 5.666666667 + 4

Combine like terms: 5.666666667 + 4 = 9.666666667
4 + -4x + x2 = 9.666666667

Factor a perfect square on the left side:
(x + -2)(x + -2) = 9.666666667

Calculate the square root of the right side: 3.109126351

Break this problem into two subproblems by setting 
(x + -2) equal to 3.109126351 and -3.109126351.

Subproblem 1

x + -2 = 3.109126351 Simplifying x + -2 = 3.109126351 Reorder the terms: -2 + x = 3.109126351 Solving -2 + x = 3.109126351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.109126351 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.109126351 + 2 x = 3.109126351 + 2 Combine like terms: 3.109126351 + 2 = 5.109126351 x = 5.109126351 Simplifying x = 5.109126351

Subproblem 2

x + -2 = -3.109126351 Simplifying x + -2 = -3.109126351 Reorder the terms: -2 + x = -3.109126351 Solving -2 + x = -3.109126351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.109126351 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.109126351 + 2 x = -3.109126351 + 2 Combine like terms: -3.109126351 + 2 = -1.109126351 x = -1.109126351 Simplifying x = -1.109126351

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.109126351, -1.109126351}

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