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

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


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

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

Reorder the terms for easier multiplication:
2(-7 + 3x) + 5(2x + 1)(x + -2) = -1x2[-1(3x + 1)]
(-7 * 2 + 3x * 2) + 5(2x + 1)(x + -2) = -1x2[-1(3x + 1)]
(-14 + 6x) + 5(2x + 1)(x + -2) = -1x2[-1(3x + 1)]

Reorder the terms:
-14 + 6x + 5(1 + 2x)(x + -2) = -1x2[-1(3x + 1)]

Reorder the terms:
-14 + 6x + 5(1 + 2x)(-2 + x) = -1x2[-1(3x + 1)]

Multiply (1 + 2x) * (-2 + x)
-14 + 6x + 5(1(-2 + x) + 2x * (-2 + x)) = -1x2[-1(3x + 1)]
-14 + 6x + 5((-2 * 1 + x * 1) + 2x * (-2 + x)) = -1x2[-1(3x + 1)]
-14 + 6x + 5((-2 + 1x) + 2x * (-2 + x)) = -1x2[-1(3x + 1)]
-14 + 6x + 5(-2 + 1x + (-2 * 2x + x * 2x)) = -1x2[-1(3x + 1)]
-14 + 6x + 5(-2 + 1x + (-4x + 2x2)) = -1x2[-1(3x + 1)]

Combine like terms: 1x + -4x = -3x
-14 + 6x + 5(-2 + -3x + 2x2) = -1x2[-1(3x + 1)]
-14 + 6x + (-2 * 5 + -3x * 5 + 2x2 * 5) = -1x2[-1(3x + 1)]
-14 + 6x + (-10 + -15x + 10x2) = -1x2[-1(3x + 1)]

Reorder the terms:
-14 + -10 + 6x + -15x + 10x2 = -1x2[-1(3x + 1)]

Combine like terms: -14 + -10 = -24
-24 + 6x + -15x + 10x2 = -1x2[-1(3x + 1)]

Combine like terms: 6x + -15x = -9x
-24 + -9x + 10x2 = -1x2[-1(3x + 1)]

Reorder the terms:
-24 + -9x + 10x2 = -1x2[-1(1 + 3x)]
-24 + -9x + 10x2 = -1x2[(1 * -1 + 3x * -1)]
-24 + -9x + 10x2 = -1x2[(-1 + -3x)]
-24 + -9x + 10x2 = [-1 * -1x2 + -3x * -1x2]
-24 + -9x + 10x2 = [1x2 + 3x3]

Solving
-24 + -9x + 10x2 = 1x2 + 3x3

Solving for variable 'x'.

Combine like terms: 10x2 + -1x2 = 9x2
-24 + -9x + 9x2 + -3x3 = 1x2 + 3x3 + -1x2 + -3x3

Reorder the terms:
-24 + -9x + 9x2 + -3x3 = 1x2 + -1x2 + 3x3 + -3x3

Combine like terms: 1x2 + -1x2 = 0
-24 + -9x + 9x2 + -3x3 = 0 + 3x3 + -3x3
-24 + -9x + 9x2 + -3x3 = 3x3 + -3x3

Combine like terms: 3x3 + -3x3 = 0
-24 + -9x + 9x2 + -3x3 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + -3x + 3x2 + -1x3) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-8 + -3x + 3x2 + -1x3)' equal to zero and attempt to solve:

Simplifying
-8 + -3x + 3x2 + -1x3 = 0

Solving
-8 + -3x + 3x2 + -1x3 = 0

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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