2x(7x-21)(x-1)=0

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Solution for 2x(7x-21)(x-1)=0 equation:


Simplifying
2x(7x + -21)(x + -1) = 0

Reorder the terms:
2x(-21 + 7x)(x + -1) = 0

Reorder the terms:
2x(-21 + 7x)(-1 + x) = 0

Multiply (-21 + 7x) * (-1 + x)
2x(-21(-1 + x) + 7x * (-1 + x)) = 0
2x((-1 * -21 + x * -21) + 7x * (-1 + x)) = 0
2x((21 + -21x) + 7x * (-1 + x)) = 0
2x(21 + -21x + (-1 * 7x + x * 7x)) = 0
2x(21 + -21x + (-7x + 7x2)) = 0

Combine like terms: -21x + -7x = -28x
2x(21 + -28x + 7x2) = 0
(21 * 2x + -28x * 2x + 7x2 * 2x) = 0
(42x + -56x2 + 14x3) = 0

Solving
42x + -56x2 + 14x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '14x'.
14x(3 + -4x + x2) = 0

Factor a trinomial.
14x((1 + -1x)(3 + -1x)) = 0

Ignore the factor 14.

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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1

Subproblem 3

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {0, 1, 3}

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