2(x+2)(x-3)=3(x+1)(x-6)+4

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Solution for 2(x+2)(x-3)=3(x+1)(x-6)+4 equation:


Simplifying
2(x + 2)(x + -3) = 3(x + 1)(x + -6) + 4

Reorder the terms:
2(2 + x)(x + -3) = 3(x + 1)(x + -6) + 4

Reorder the terms:
2(2 + x)(-3 + x) = 3(x + 1)(x + -6) + 4

Multiply (2 + x) * (-3 + x)
2(2(-3 + x) + x(-3 + x)) = 3(x + 1)(x + -6) + 4
2((-3 * 2 + x * 2) + x(-3 + x)) = 3(x + 1)(x + -6) + 4
2((-6 + 2x) + x(-3 + x)) = 3(x + 1)(x + -6) + 4
2(-6 + 2x + (-3 * x + x * x)) = 3(x + 1)(x + -6) + 4
2(-6 + 2x + (-3x + x2)) = 3(x + 1)(x + -6) + 4

Combine like terms: 2x + -3x = -1x
2(-6 + -1x + x2) = 3(x + 1)(x + -6) + 4
(-6 * 2 + -1x * 2 + x2 * 2) = 3(x + 1)(x + -6) + 4
(-12 + -2x + 2x2) = 3(x + 1)(x + -6) + 4

Reorder the terms:
-12 + -2x + 2x2 = 3(1 + x)(x + -6) + 4

Reorder the terms:
-12 + -2x + 2x2 = 3(1 + x)(-6 + x) + 4

Multiply (1 + x) * (-6 + x)
-12 + -2x + 2x2 = 3(1(-6 + x) + x(-6 + x)) + 4
-12 + -2x + 2x2 = 3((-6 * 1 + x * 1) + x(-6 + x)) + 4
-12 + -2x + 2x2 = 3((-6 + 1x) + x(-6 + x)) + 4
-12 + -2x + 2x2 = 3(-6 + 1x + (-6 * x + x * x)) + 4
-12 + -2x + 2x2 = 3(-6 + 1x + (-6x + x2)) + 4

Combine like terms: 1x + -6x = -5x
-12 + -2x + 2x2 = 3(-6 + -5x + x2) + 4
-12 + -2x + 2x2 = (-6 * 3 + -5x * 3 + x2 * 3) + 4
-12 + -2x + 2x2 = (-18 + -15x + 3x2) + 4

Reorder the terms:
-12 + -2x + 2x2 = -18 + 4 + -15x + 3x2

Combine like terms: -18 + 4 = -14
-12 + -2x + 2x2 = -14 + -15x + 3x2

Solving
-12 + -2x + 2x2 = -14 + -15x + 3x2

Solving for variable 'x'.

Reorder the terms:
-12 + 14 + -2x + 15x + 2x2 + -3x2 = -14 + -15x + 3x2 + 14 + 15x + -3x2

Combine like terms: -12 + 14 = 2
2 + -2x + 15x + 2x2 + -3x2 = -14 + -15x + 3x2 + 14 + 15x + -3x2

Combine like terms: -2x + 15x = 13x
2 + 13x + 2x2 + -3x2 = -14 + -15x + 3x2 + 14 + 15x + -3x2

Combine like terms: 2x2 + -3x2 = -1x2
2 + 13x + -1x2 = -14 + -15x + 3x2 + 14 + 15x + -3x2

Reorder the terms:
2 + 13x + -1x2 = -14 + 14 + -15x + 15x + 3x2 + -3x2

Combine like terms: -14 + 14 = 0
2 + 13x + -1x2 = 0 + -15x + 15x + 3x2 + -3x2
2 + 13x + -1x2 = -15x + 15x + 3x2 + -3x2

Combine like terms: -15x + 15x = 0
2 + 13x + -1x2 = 0 + 3x2 + -3x2
2 + 13x + -1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
2 + 13x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2 + -13x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -13x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -13x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -13x + x2 = 0 + 2
-13x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-13x + x2 = 2

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = 2 + 42.25

Reorder the terms:
42.25 + -13x + x2 = 2 + 42.25

Combine like terms: 2 + 42.25 = 44.25
42.25 + -13x + x2 = 44.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 44.25

Calculate the square root of the right side: 6.652067348

Break this problem into two subproblems by setting 
(x + -6.5) equal to 6.652067348 and -6.652067348.

Subproblem 1

x + -6.5 = 6.652067348 Simplifying x + -6.5 = 6.652067348 Reorder the terms: -6.5 + x = 6.652067348 Solving -6.5 + x = 6.652067348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 6.652067348 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 6.652067348 + 6.5 x = 6.652067348 + 6.5 Combine like terms: 6.652067348 + 6.5 = 13.152067348 x = 13.152067348 Simplifying x = 13.152067348

Subproblem 2

x + -6.5 = -6.652067348 Simplifying x + -6.5 = -6.652067348 Reorder the terms: -6.5 + x = -6.652067348 Solving -6.5 + x = -6.652067348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -6.652067348 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -6.652067348 + 6.5 x = -6.652067348 + 6.5 Combine like terms: -6.652067348 + 6.5 = -0.152067348 x = -0.152067348 Simplifying x = -0.152067348

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.152067348, -0.152067348}

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