1=6x^2-x

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Solution for 1=6x^2-x equation:


Simplifying
1 = 6x2 + -1x

Reorder the terms:
1 = -1x + 6x2

Solving
1 = -1x + 6x2

Solving for variable 'x'.

Reorder the terms:
1 + x + -6x2 = -1x + x + 6x2 + -6x2

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

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

Factor a trinomial.
(1 + -2x)(1 + 3x) = 0

Subproblem 1

Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5

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 = {0.5, -0.3333333333}

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