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

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


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

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

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

Multiply (2 + x) * (-3 + x)
5 = -3(2(-3 + x) + x(-3 + x))
5 = -3((-3 * 2 + x * 2) + x(-3 + x))
5 = -3((-6 + 2x) + x(-3 + x))
5 = -3(-6 + 2x + (-3 * x + x * x))
5 = -3(-6 + 2x + (-3x + x2))

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

Solving
5 = 18 + 3x + -3x2

Solving for variable 'x'.

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

Reorder the terms:
-13 + -3x + 3x2 = 18 + -18 + 3x + -3x + -3x2 + 3x2

Combine like terms: 18 + -18 = 0
-13 + -3x + 3x2 = 0 + 3x + -3x + -3x2 + 3x2
-13 + -3x + 3x2 = 3x + -3x + -3x2 + 3x2

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

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

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

Divide each side by '3'.
-4.333333333 + -1x + x2 = 0

Move the constant term to the right:

Add '4.333333333' to each side of the equation.
-4.333333333 + -1x + 4.333333333 + x2 = 0 + 4.333333333

Reorder the terms:
-4.333333333 + 4.333333333 + -1x + x2 = 0 + 4.333333333

Combine like terms: -4.333333333 + 4.333333333 = 0.000000000
0.000000000 + -1x + x2 = 0 + 4.333333333
-1x + x2 = 0 + 4.333333333

Combine like terms: 0 + 4.333333333 = 4.333333333
-1x + x2 = 4.333333333

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 4.333333333 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 4.333333333 + 0.25

Combine like terms: 4.333333333 + 0.25 = 4.583333333
0.25 + -1x + x2 = 4.583333333

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 4.583333333

Calculate the square root of the right side: 2.140872096

Break this problem into two subproblems by setting 
(x + -0.5) equal to 2.140872096 and -2.140872096.

Subproblem 1

x + -0.5 = 2.140872096 Simplifying x + -0.5 = 2.140872096 Reorder the terms: -0.5 + x = 2.140872096 Solving -0.5 + x = 2.140872096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 2.140872096 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.140872096 + 0.5 x = 2.140872096 + 0.5 Combine like terms: 2.140872096 + 0.5 = 2.640872096 x = 2.640872096 Simplifying x = 2.640872096

Subproblem 2

x + -0.5 = -2.140872096 Simplifying x + -0.5 = -2.140872096 Reorder the terms: -0.5 + x = -2.140872096 Solving -0.5 + x = -2.140872096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -2.140872096 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.140872096 + 0.5 x = -2.140872096 + 0.5 Combine like terms: -2.140872096 + 0.5 = -1.640872096 x = -1.640872096 Simplifying x = -1.640872096

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.640872096, -1.640872096}

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