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

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


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

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

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

Combine like terms: 2x + -15x = -13x
(10 + -13x + -3x2) = 3(x + -2) * 2 + -1x

Reorder the terms:
10 + -13x + -3x2 = 3(-2 + x) * 2 + -1x

Reorder the terms for easier multiplication:
10 + -13x + -3x2 = 3 * 2(-2 + x) + -1x

Multiply 3 * 2
10 + -13x + -3x2 = 6(-2 + x) + -1x
10 + -13x + -3x2 = (-2 * 6 + x * 6) + -1x
10 + -13x + -3x2 = (-12 + 6x) + -1x

Combine like terms: 6x + -1x = 5x
10 + -13x + -3x2 = -12 + 5x

Solving
10 + -13x + -3x2 = -12 + 5x

Solving for variable 'x'.

Reorder the terms:
10 + 12 + -13x + -5x + -3x2 = -12 + 5x + 12 + -5x

Combine like terms: 10 + 12 = 22
22 + -13x + -5x + -3x2 = -12 + 5x + 12 + -5x

Combine like terms: -13x + -5x = -18x
22 + -18x + -3x2 = -12 + 5x + 12 + -5x

Reorder the terms:
22 + -18x + -3x2 = -12 + 12 + 5x + -5x

Combine like terms: -12 + 12 = 0
22 + -18x + -3x2 = 0 + 5x + -5x
22 + -18x + -3x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
22 + -18x + -3x2 = 0

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

Divide each side by '-3'.
-7.333333333 + 6x + x2 = 0

Move the constant term to the right:

Add '7.333333333' to each side of the equation.
-7.333333333 + 6x + 7.333333333 + x2 = 0 + 7.333333333

Reorder the terms:
-7.333333333 + 7.333333333 + 6x + x2 = 0 + 7.333333333

Combine like terms: -7.333333333 + 7.333333333 = 0.000000000
0.000000000 + 6x + x2 = 0 + 7.333333333
6x + x2 = 0 + 7.333333333

Combine like terms: 0 + 7.333333333 = 7.333333333
6x + x2 = 7.333333333

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 7.333333333 + 9

Reorder the terms:
9 + 6x + x2 = 7.333333333 + 9

Combine like terms: 7.333333333 + 9 = 16.333333333
9 + 6x + x2 = 16.333333333

Factor a perfect square on the left side:
(x + 3)(x + 3) = 16.333333333

Calculate the square root of the right side: 4.041451884

Break this problem into two subproblems by setting 
(x + 3) equal to 4.041451884 and -4.041451884.

Subproblem 1

x + 3 = 4.041451884 Simplifying x + 3 = 4.041451884 Reorder the terms: 3 + x = 4.041451884 Solving 3 + x = 4.041451884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 4.041451884 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.041451884 + -3 x = 4.041451884 + -3 Combine like terms: 4.041451884 + -3 = 1.041451884 x = 1.041451884 Simplifying x = 1.041451884

Subproblem 2

x + 3 = -4.041451884 Simplifying x + 3 = -4.041451884 Reorder the terms: 3 + x = -4.041451884 Solving 3 + x = -4.041451884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -4.041451884 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.041451884 + -3 x = -4.041451884 + -3 Combine like terms: -4.041451884 + -3 = -7.041451884 x = -7.041451884 Simplifying x = -7.041451884

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.041451884, -7.041451884}

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