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

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


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

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

Remove parenthesis around (-3 + 3x)
-3 + 3x + -1(2x + -7) = (3x + -5)(3x + 5)

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

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

Combine like terms: -3 + 7 = 4
4 + 3x + -2x = (3x + -5)(3x + 5)

Combine like terms: 3x + -2x = 1x
4 + 1x = (3x + -5)(3x + 5)

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

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

Multiply (-5 + 3x) * (5 + 3x)
4 + 1x = (-5(5 + 3x) + 3x * (5 + 3x))
4 + 1x = ((5 * -5 + 3x * -5) + 3x * (5 + 3x))
4 + 1x = ((-25 + -15x) + 3x * (5 + 3x))
4 + 1x = (-25 + -15x + (5 * 3x + 3x * 3x))
4 + 1x = (-25 + -15x + (15x + 9x2))

Combine like terms: -15x + 15x = 0
4 + 1x = (-25 + 0 + 9x2)
4 + 1x = (-25 + 9x2)

Solving
4 + 1x = -25 + 9x2

Solving for variable 'x'.

Reorder the terms:
4 + 25 + 1x + -9x2 = -25 + 9x2 + 25 + -9x2

Combine like terms: 4 + 25 = 29
29 + 1x + -9x2 = -25 + 9x2 + 25 + -9x2

Reorder the terms:
29 + 1x + -9x2 = -25 + 25 + 9x2 + -9x2

Combine like terms: -25 + 25 = 0
29 + 1x + -9x2 = 0 + 9x2 + -9x2
29 + 1x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
29 + 1x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-3.222222222 + -0.1111111111x + x2 = 0

Move the constant term to the right:

Add '3.222222222' to each side of the equation.
-3.222222222 + -0.1111111111x + 3.222222222 + x2 = 0 + 3.222222222

Reorder the terms:
-3.222222222 + 3.222222222 + -0.1111111111x + x2 = 0 + 3.222222222

Combine like terms: -3.222222222 + 3.222222222 = 0.000000000
0.000000000 + -0.1111111111x + x2 = 0 + 3.222222222
-0.1111111111x + x2 = 0 + 3.222222222

Combine like terms: 0 + 3.222222222 = 3.222222222
-0.1111111111x + x2 = 3.222222222

The x term is -0.1111111111x.  Take half its coefficient (-0.05555555555).
Square it (0.003086419752) and add it to both sides.

Add '0.003086419752' to each side of the equation.
-0.1111111111x + 0.003086419752 + x2 = 3.222222222 + 0.003086419752

Reorder the terms:
0.003086419752 + -0.1111111111x + x2 = 3.222222222 + 0.003086419752

Combine like terms: 3.222222222 + 0.003086419752 = 3.225308641752
0.003086419752 + -0.1111111111x + x2 = 3.225308641752

Factor a perfect square on the left side:
(x + -0.05555555555)(x + -0.05555555555) = 3.225308641752

Calculate the square root of the right side: 1.795914431

Break this problem into two subproblems by setting 
(x + -0.05555555555) equal to 1.795914431 and -1.795914431.

Subproblem 1

x + -0.05555555555 = 1.795914431 Simplifying x + -0.05555555555 = 1.795914431 Reorder the terms: -0.05555555555 + x = 1.795914431 Solving -0.05555555555 + x = 1.795914431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + x = 1.795914431 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = 1.795914431 + 0.05555555555 x = 1.795914431 + 0.05555555555 Combine like terms: 1.795914431 + 0.05555555555 = 1.85146998655 x = 1.85146998655 Simplifying x = 1.85146998655

Subproblem 2

x + -0.05555555555 = -1.795914431 Simplifying x + -0.05555555555 = -1.795914431 Reorder the terms: -0.05555555555 + x = -1.795914431 Solving -0.05555555555 + x = -1.795914431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + x = -1.795914431 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = -1.795914431 + 0.05555555555 x = -1.795914431 + 0.05555555555 Combine like terms: -1.795914431 + 0.05555555555 = -1.74035887545 x = -1.74035887545 Simplifying x = -1.74035887545

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.85146998655, -1.74035887545}

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