2x-1=6x^2+x-8

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Solution for 2x-1=6x^2+x-8 equation:


Simplifying
2x + -1 = 6x2 + x + -8

Reorder the terms:
-1 + 2x = 6x2 + x + -8

Reorder the terms:
-1 + 2x = -8 + x + 6x2

Solving
-1 + 2x = -8 + x + 6x2

Solving for variable 'x'.

Reorder the terms:
-1 + 8 + 2x + -1x + -6x2 = -8 + x + 6x2 + 8 + -1x + -6x2

Combine like terms: -1 + 8 = 7
7 + 2x + -1x + -6x2 = -8 + x + 6x2 + 8 + -1x + -6x2

Combine like terms: 2x + -1x = 1x
7 + 1x + -6x2 = -8 + x + 6x2 + 8 + -1x + -6x2

Reorder the terms:
7 + 1x + -6x2 = -8 + 8 + x + -1x + 6x2 + -6x2

Combine like terms: -8 + 8 = 0
7 + 1x + -6x2 = 0 + x + -1x + 6x2 + -6x2
7 + 1x + -6x2 = x + -1x + 6x2 + -6x2

Combine like terms: x + -1x = 0
7 + 1x + -6x2 = 0 + 6x2 + -6x2
7 + 1x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
7 + 1x + -6x2 = 0

Factor a trinomial.
(7 + -6x)(1 + x) = 0

Subproblem 1

Set the factor '(7 + -6x)' equal to zero and attempt to solve: Simplifying 7 + -6x = 0 Solving 7 + -6x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -6x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6x = 0 + -7 -6x = 0 + -7 Combine like terms: 0 + -7 = -7 -6x = -7 Divide each side by '-6'. x = 1.166666667 Simplifying x = 1.166666667

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {1.166666667, -1}

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