F(x)=(x^3-2x)(5x-7)

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


Simplifying
F(x) = (x3 + -2x)(5x + -7)

Multiply F * x
xF = (x3 + -2x)(5x + -7)

Reorder the terms:
xF = (-2x + x3)(5x + -7)

Reorder the terms:
xF = (-2x + x3)(-7 + 5x)

Multiply (-2x + x3) * (-7 + 5x)
xF = (-2x * (-7 + 5x) + x3(-7 + 5x))
xF = ((-7 * -2x + 5x * -2x) + x3(-7 + 5x))
xF = ((14x + -10x2) + x3(-7 + 5x))
xF = (14x + -10x2 + (-7 * x3 + 5x * x3))
xF = (14x + -10x2 + (-7x3 + 5x4))
xF = (14x + -10x2 + -7x3 + 5x4)

Solving
xF = 14x + -10x2 + -7x3 + 5x4

Solving for variable 'x'.

Reorder the terms:
-14x + xF + 10x2 + 7x3 + -5x4 = 14x + -10x2 + -7x3 + 5x4 + -14x + 10x2 + 7x3 + -5x4

Reorder the terms:
-14x + xF + 10x2 + 7x3 + -5x4 = 14x + -14x + -10x2 + 10x2 + -7x3 + 7x3 + 5x4 + -5x4

Combine like terms: 14x + -14x = 0
-14x + xF + 10x2 + 7x3 + -5x4 = 0 + -10x2 + 10x2 + -7x3 + 7x3 + 5x4 + -5x4
-14x + xF + 10x2 + 7x3 + -5x4 = -10x2 + 10x2 + -7x3 + 7x3 + 5x4 + -5x4

Combine like terms: -10x2 + 10x2 = 0
-14x + xF + 10x2 + 7x3 + -5x4 = 0 + -7x3 + 7x3 + 5x4 + -5x4
-14x + xF + 10x2 + 7x3 + -5x4 = -7x3 + 7x3 + 5x4 + -5x4

Combine like terms: -7x3 + 7x3 = 0
-14x + xF + 10x2 + 7x3 + -5x4 = 0 + 5x4 + -5x4
-14x + xF + 10x2 + 7x3 + -5x4 = 5x4 + -5x4

Combine like terms: 5x4 + -5x4 = 0
-14x + xF + 10x2 + 7x3 + -5x4 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-14 + F + 10x + 7x2 + -5x3) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(-14 + F + 10x + 7x2 + -5x3)' equal to zero and attempt to solve: Simplifying -14 + F + 10x + 7x2 + -5x3 = 0 Solving -14 + F + 10x + 7x2 + -5x3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

x = {0}

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