5x(x-9)=11x^2-46x

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Solution for 5x(x-9)=11x^2-46x equation: 


Simplifying
5x(x + -9) = 11x2 + -46x

Reorder the terms:
5x(-9 + x) = 11x2 + -46x
(-9 * 5x + x * 5x) = 11x2 + -46x
(-45x + 5x2) = 11x2 + -46x

Reorder the terms:
-45x + 5x2 = -46x + 11x2

Solving
-45x + 5x2 = -46x + 11x2

Solving for variable 'x'.

Reorder the terms:
-45x + 46x + 5x2 + -11x2 = -46x + 11x2 + 46x + -11x2

Combine like terms: -45x + 46x = 1x
1x + 5x2 + -11x2 = -46x + 11x2 + 46x + -11x2

Combine like terms: 5x2 + -11x2 = -6x2
1x + -6x2 = -46x + 11x2 + 46x + -11x2

Reorder the terms:
1x + -6x2 = -46x + 46x + 11x2 + -11x2

Combine like terms: -46x + 46x = 0
1x + -6x2 = 0 + 11x2 + -11x2
1x + -6x2 = 11x2 + -11x2

Combine like terms: 11x2 + -11x2 = 0
1x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -6x) = 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 + -6x)' equal to zero and attempt to solve:

Simplifying
1 + -6x = 0

Solving
1 + -6x = 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 + -6x = 0 + -1

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

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

Divide each side by '-6'.
x = 0.1666666667

Simplifying
x = 0.1666666667
Solution
x = {0, 0.1666666667}

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