(4x+5)(3x-7)-(x+2)(4x-2)=72-33x

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Solution for (4x+5)(3x-7)-(x+2)(4x-2)=72-33x equation: 


Simplifying
(4x + 5)(3x + -7) + -1(x + 2)(4x + -2) = 72 + -33x

Reorder the terms:
(5 + 4x)(3x + -7) + -1(x + 2)(4x + -2) = 72 + -33x

Reorder the terms:
(5 + 4x)(-7 + 3x) + -1(x + 2)(4x + -2) = 72 + -33x

Multiply (5 + 4x) * (-7 + 3x)
(5(-7 + 3x) + 4x * (-7 + 3x)) + -1(x + 2)(4x + -2) = 72 + -33x
((-7 * 5 + 3x * 5) + 4x * (-7 + 3x)) + -1(x + 2)(4x + -2) = 72 + -33x
((-35 + 15x) + 4x * (-7 + 3x)) + -1(x + 2)(4x + -2) = 72 + -33x
(-35 + 15x + (-7 * 4x + 3x * 4x)) + -1(x + 2)(4x + -2) = 72 + -33x
(-35 + 15x + (-28x + 12x2)) + -1(x + 2)(4x + -2) = 72 + -33x

Combine like terms: 15x + -28x = -13x
(-35 + -13x + 12x2) + -1(x + 2)(4x + -2) = 72 + -33x

Reorder the terms:
-35 + -13x + 12x2 + -1(2 + x)(4x + -2) = 72 + -33x

Reorder the terms:
-35 + -13x + 12x2 + -1(2 + x)(-2 + 4x) = 72 + -33x

Multiply (2 + x) * (-2 + 4x)
-35 + -13x + 12x2 + -1(2(-2 + 4x) + x(-2 + 4x)) = 72 + -33x
-35 + -13x + 12x2 + -1((-2 * 2 + 4x * 2) + x(-2 + 4x)) = 72 + -33x
-35 + -13x + 12x2 + -1((-4 + 8x) + x(-2 + 4x)) = 72 + -33x
-35 + -13x + 12x2 + -1(-4 + 8x + (-2 * x + 4x * x)) = 72 + -33x
-35 + -13x + 12x2 + -1(-4 + 8x + (-2x + 4x2)) = 72 + -33x

Combine like terms: 8x + -2x = 6x
-35 + -13x + 12x2 + -1(-4 + 6x + 4x2) = 72 + -33x
-35 + -13x + 12x2 + (-4 * -1 + 6x * -1 + 4x2 * -1) = 72 + -33x
-35 + -13x + 12x2 + (4 + -6x + -4x2) = 72 + -33x

Reorder the terms:
-35 + 4 + -13x + -6x + 12x2 + -4x2 = 72 + -33x

Combine like terms: -35 + 4 = -31
-31 + -13x + -6x + 12x2 + -4x2 = 72 + -33x

Combine like terms: -13x + -6x = -19x
-31 + -19x + 12x2 + -4x2 = 72 + -33x

Combine like terms: 12x2 + -4x2 = 8x2
-31 + -19x + 8x2 = 72 + -33x

Solving
-31 + -19x + 8x2 = 72 + -33x

Solving for variable 'x'.

Reorder the terms:
-31 + -72 + -19x + 33x + 8x2 = 72 + -33x + -72 + 33x

Combine like terms: -31 + -72 = -103
-103 + -19x + 33x + 8x2 = 72 + -33x + -72 + 33x

Combine like terms: -19x + 33x = 14x
-103 + 14x + 8x2 = 72 + -33x + -72 + 33x

Reorder the terms:
-103 + 14x + 8x2 = 72 + -72 + -33x + 33x

Combine like terms: 72 + -72 = 0
-103 + 14x + 8x2 = 0 + -33x + 33x
-103 + 14x + 8x2 = -33x + 33x

Combine like terms: -33x + 33x = 0
-103 + 14x + 8x2 = 0

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

Divide each side by '8'.
-12.875 + 1.75x + x2 = 0

Move the constant term to the right:

Add '12.875' to each side of the equation.
-12.875 + 1.75x + 12.875 + x2 = 0 + 12.875

Reorder the terms:
-12.875 + 12.875 + 1.75x + x2 = 0 + 12.875

Combine like terms: -12.875 + 12.875 = 0.000
0.000 + 1.75x + x2 = 0 + 12.875
1.75x + x2 = 0 + 12.875

Combine like terms: 0 + 12.875 = 12.875
1.75x + x2 = 12.875

The x term is 1.75x.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75x + 0.765625 + x2 = 12.875 + 0.765625

Reorder the terms:
0.765625 + 1.75x + x2 = 12.875 + 0.765625

Combine like terms: 12.875 + 0.765625 = 13.640625
0.765625 + 1.75x + x2 = 13.640625

Factor a perfect square on the left side:
(x + 0.875)(x + 0.875) = 13.640625

Calculate the square root of the right side: 3.693321676

Break this problem into two subproblems by setting 
(x + 0.875) equal to 3.693321676 and -3.693321676.


Subproblem 1
x + 0.875 = 3.693321676

Simplifying
x + 0.875 = 3.693321676

Reorder the terms:
0.875 + x = 3.693321676

Solving
0.875 + x = 3.693321676

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.875' to each side of the equation.
0.875 + -0.875 + x = 3.693321676 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + x = 3.693321676 + -0.875
x = 3.693321676 + -0.875

Combine like terms: 3.693321676 + -0.875 = 2.818321676
x = 2.818321676

Simplifying
x = 2.818321676


Subproblem 2
x + 0.875 = -3.693321676

Simplifying
x + 0.875 = -3.693321676

Reorder the terms:
0.875 + x = -3.693321676

Solving
0.875 + x = -3.693321676

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.875' to each side of the equation.
0.875 + -0.875 + x = -3.693321676 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + x = -3.693321676 + -0.875
x = -3.693321676 + -0.875

Combine like terms: -3.693321676 + -0.875 = -4.568321676
x = -4.568321676

Simplifying
x = -4.568321676


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.818321676, -4.568321676}

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