6x^2-9x=11x-9x^2

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Solution for 6x^2-9x=11x-9x^2 equation:


Simplifying
6x2 + -9x = 11x + -9x2

Reorder the terms:
-9x + 6x2 = 11x + -9x2

Solving
-9x + 6x2 = 11x + -9x2

Solving for variable 'x'.

Reorder the terms:
-9x + -11x + 6x2 + 9x2 = 11x + -9x2 + -11x + 9x2

Combine like terms: -9x + -11x = -20x
-20x + 6x2 + 9x2 = 11x + -9x2 + -11x + 9x2

Combine like terms: 6x2 + 9x2 = 15x2
-20x + 15x2 = 11x + -9x2 + -11x + 9x2

Reorder the terms:
-20x + 15x2 = 11x + -11x + -9x2 + 9x2

Combine like terms: 11x + -11x = 0
-20x + 15x2 = 0 + -9x2 + 9x2
-20x + 15x2 = -9x2 + 9x2

Combine like terms: -9x2 + 9x2 = 0
-20x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-4 + 3x) = 0

Ignore the factor 5.

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 '(-4 + 3x)' equal to zero and attempt to solve: Simplifying -4 + 3x = 0 Solving -4 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + 3x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 3x = 0 + 4 3x = 0 + 4 Combine like terms: 0 + 4 = 4 3x = 4 Divide each side by '3'. x = 1.333333333 Simplifying x = 1.333333333

Solution

x = {0, 1.333333333}

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