21x^2+1=1-7x

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Solution for 21x^2+1=1-7x equation:


Simplifying
21x2 + 1 = 1 + -7x

Reorder the terms:
1 + 21x2 = 1 + -7x

Add '-1' to each side of the equation.
1 + -1 + 21x2 = 1 + -1 + -7x

Combine like terms: 1 + -1 = 0
0 + 21x2 = 1 + -1 + -7x
21x2 = 1 + -1 + -7x

Combine like terms: 1 + -1 = 0
21x2 = 0 + -7x
21x2 = -7x

Solving
21x2 = -7x

Solving for variable 'x'.

Reorder the terms:
7x + 21x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
7x + 21x2 = 0

Factor out the Greatest Common Factor (GCF), '7x'.
7x(1 + 3x) = 0

Ignore the factor 7.

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 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333

Solution

x = {0, -0.3333333333}

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