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

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


Simplifying
7(x + -3) + -5(x2 + -1) = x2 + -1(5x + 2)

Reorder the terms:
7(-3 + x) + -5(x2 + -1) = x2 + -1(5x + 2)
(-3 * 7 + x * 7) + -5(x2 + -1) = x2 + -1(5x + 2)
(-21 + 7x) + -5(x2 + -1) = x2 + -1(5x + 2)

Reorder the terms:
-21 + 7x + -5(-1 + x2) = x2 + -1(5x + 2)
-21 + 7x + (-1 * -5 + x2 * -5) = x2 + -1(5x + 2)
-21 + 7x + (5 + -5x2) = x2 + -1(5x + 2)

Reorder the terms:
-21 + 5 + 7x + -5x2 = x2 + -1(5x + 2)

Combine like terms: -21 + 5 = -16
-16 + 7x + -5x2 = x2 + -1(5x + 2)

Reorder the terms:
-16 + 7x + -5x2 = x2 + -1(2 + 5x)
-16 + 7x + -5x2 = x2 + (2 * -1 + 5x * -1)
-16 + 7x + -5x2 = x2 + (-2 + -5x)

Reorder the terms:
-16 + 7x + -5x2 = -2 + -5x + x2

Solving
-16 + 7x + -5x2 = -2 + -5x + x2

Solving for variable 'x'.

Reorder the terms:
-16 + 2 + 7x + 5x + -5x2 + -1x2 = -2 + -5x + x2 + 2 + 5x + -1x2

Combine like terms: -16 + 2 = -14
-14 + 7x + 5x + -5x2 + -1x2 = -2 + -5x + x2 + 2 + 5x + -1x2

Combine like terms: 7x + 5x = 12x
-14 + 12x + -5x2 + -1x2 = -2 + -5x + x2 + 2 + 5x + -1x2

Combine like terms: -5x2 + -1x2 = -6x2
-14 + 12x + -6x2 = -2 + -5x + x2 + 2 + 5x + -1x2

Reorder the terms:
-14 + 12x + -6x2 = -2 + 2 + -5x + 5x + x2 + -1x2

Combine like terms: -2 + 2 = 0
-14 + 12x + -6x2 = 0 + -5x + 5x + x2 + -1x2
-14 + 12x + -6x2 = -5x + 5x + x2 + -1x2

Combine like terms: -5x + 5x = 0
-14 + 12x + -6x2 = 0 + x2 + -1x2
-14 + 12x + -6x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-14 + 12x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 6x + -3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + 6x + -3x2)' equal to zero and attempt to solve:

Simplifying
-7 + 6x + -3x2 = 0

Solving
-7 + 6x + -3x2 = 0

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

Divide each side by '-3'.
2.333333333 + -2x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -2x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -2x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -2x + x2 = 0 + -2.333333333
-2x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-2x + x2 = -2.333333333

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -2.333333333 + 1

Reorder the terms:
1 + -2x + x2 = -2.333333333 + 1

Combine like terms: -2.333333333 + 1 = -1.333333333
1 + -2x + x2 = -1.333333333

Factor a perfect square on the left side:
(x + -1)(x + -1) = -1.333333333

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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