-1-6x^2-4x=2x^2+5x

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Solution for -1-6x^2-4x=2x^2+5x equation:


Simplifying
-1 + -6x2 + -4x = 2x2 + 5x

Reorder the terms:
-1 + -4x + -6x2 = 2x2 + 5x

Reorder the terms:
-1 + -4x + -6x2 = 5x + 2x2

Solving
-1 + -4x + -6x2 = 5x + 2x2

Solving for variable 'x'.

Reorder the terms:
-1 + -4x + -5x + -6x2 + -2x2 = 5x + 2x2 + -5x + -2x2

Combine like terms: -4x + -5x = -9x
-1 + -9x + -6x2 + -2x2 = 5x + 2x2 + -5x + -2x2

Combine like terms: -6x2 + -2x2 = -8x2
-1 + -9x + -8x2 = 5x + 2x2 + -5x + -2x2

Reorder the terms:
-1 + -9x + -8x2 = 5x + -5x + 2x2 + -2x2

Combine like terms: 5x + -5x = 0
-1 + -9x + -8x2 = 0 + 2x2 + -2x2
-1 + -9x + -8x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-1 + -9x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 9x + 8x2) = 0

Factor a trinomial.
-1((1 + x)(1 + 8x)) = 0

Ignore the factor -1.

Subproblem 1

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

Subproblem 2

Set the factor '(1 + 8x)' equal to zero and attempt to solve: Simplifying 1 + 8x = 0 Solving 1 + 8x = 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 + 8x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 8x = 0 + -1 8x = 0 + -1 Combine like terms: 0 + -1 = -1 8x = -1 Divide each side by '8'. x = -0.125 Simplifying x = -0.125

Solution

x = {-1, -0.125}

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