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

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Solution for 2(3x-7)(2x+1)-(5x-2)2= equation: 


Simplifying
2(3x + -7)(2x + 1) + -1(5x + -2) * 2 = 0

Reorder the terms:
2(-7 + 3x)(2x + 1) + -1(5x + -2) * 2 = 0

Reorder the terms:
2(-7 + 3x)(1 + 2x) + -1(5x + -2) * 2 = 0

Multiply (-7 + 3x) * (1 + 2x)
2(-7(1 + 2x) + 3x * (1 + 2x)) + -1(5x + -2) * 2 = 0
2((1 * -7 + 2x * -7) + 3x * (1 + 2x)) + -1(5x + -2) * 2 = 0
2((-7 + -14x) + 3x * (1 + 2x)) + -1(5x + -2) * 2 = 0
2(-7 + -14x + (1 * 3x + 2x * 3x)) + -1(5x + -2) * 2 = 0
2(-7 + -14x + (3x + 6x2)) + -1(5x + -2) * 2 = 0

Combine like terms: -14x + 3x = -11x
2(-7 + -11x + 6x2) + -1(5x + -2) * 2 = 0
(-7 * 2 + -11x * 2 + 6x2 * 2) + -1(5x + -2) * 2 = 0
(-14 + -22x + 12x2) + -1(5x + -2) * 2 = 0

Reorder the terms:
-14 + -22x + 12x2 + -1(-2 + 5x) * 2 = 0

Reorder the terms for easier multiplication:
-14 + -22x + 12x2 + -1 * 2(-2 + 5x) = 0

Multiply -1 * 2
-14 + -22x + 12x2 + -2(-2 + 5x) = 0
-14 + -22x + 12x2 + (-2 * -2 + 5x * -2) = 0
-14 + -22x + 12x2 + (4 + -10x) = 0

Reorder the terms:
-14 + 4 + -22x + -10x + 12x2 = 0

Combine like terms: -14 + 4 = -10
-10 + -22x + -10x + 12x2 = 0

Combine like terms: -22x + -10x = -32x
-10 + -32x + 12x2 = 0

Solving
-10 + -32x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -16x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + -16x + 6x2)' equal to zero and attempt to solve:

Simplifying
-5 + -16x + 6x2 = 0

Solving
-5 + -16x + 6x2 = 0

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

Divide each side by '6'.
-0.8333333333 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -2.666666667x + 0.8333333333 + x2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -2.666666667x + x2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -2.666666667x + x2 = 0 + 0.8333333333
-2.666666667x + x2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-2.666666667x + x2 = 0.8333333333

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = 0.8333333333 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = 0.8333333333 + 1.777777780

Combine like terms: 0.8333333333 + 1.777777780 = 2.6111111133
1.777777780 + -2.666666667x + x2 = 2.6111111133

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 2.6111111133

Calculate the square root of the right side: 1.615893286

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 1.615893286 and -1.615893286.


Subproblem 1
x + -1.333333334 = 1.615893286

Simplifying
x + -1.333333334 = 1.615893286

Reorder the terms:
-1.333333334 + x = 1.615893286

Solving
-1.333333334 + x = 1.615893286

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = 1.615893286 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = 1.615893286 + 1.333333334
x = 1.615893286 + 1.333333334

Combine like terms: 1.615893286 + 1.333333334 = 2.94922662
x = 2.94922662

Simplifying
x = 2.94922662


Subproblem 2
x + -1.333333334 = -1.615893286

Simplifying
x + -1.333333334 = -1.615893286

Reorder the terms:
-1.333333334 + x = -1.615893286

Solving
-1.333333334 + x = -1.615893286

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = -1.615893286 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = -1.615893286 + 1.333333334
x = -1.615893286 + 1.333333334

Combine like terms: -1.615893286 + 1.333333334 = -0.282559952
x = -0.282559952

Simplifying
x = -0.282559952


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.94922662, -0.282559952}
Solution
x = {2.94922662, -0.282559952}

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