6x=5x-2x^2

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Solution for 6x=5x-2x^2 equation:


Simplifying
6x = 5x + -2x2

Solving
6x = 5x + -2x2

Solving for variable 'x'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + 2x) = 0

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 + 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

Solution

x = {0, -0.5}

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