3x(x-9)=13x^2-28x

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Solution for 3x(x-9)=13x^2-28x equation: 


Simplifying
3x(x + -9) = 13x2 + -28x

Reorder the terms:
3x(-9 + x) = 13x2 + -28x
(-9 * 3x + x * 3x) = 13x2 + -28x
(-27x + 3x2) = 13x2 + -28x

Reorder the terms:
-27x + 3x2 = -28x + 13x2

Solving
-27x + 3x2 = -28x + 13x2

Solving for variable 'x'.

Reorder the terms:
-27x + 28x + 3x2 + -13x2 = -28x + 13x2 + 28x + -13x2

Combine like terms: -27x + 28x = 1x
1x + 3x2 + -13x2 = -28x + 13x2 + 28x + -13x2

Combine like terms: 3x2 + -13x2 = -10x2
1x + -10x2 = -28x + 13x2 + 28x + -13x2

Reorder the terms:
1x + -10x2 = -28x + 28x + 13x2 + -13x2

Combine like terms: -28x + 28x = 0
1x + -10x2 = 0 + 13x2 + -13x2
1x + -10x2 = 13x2 + -13x2

Combine like terms: 13x2 + -13x2 = 0
1x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -10x) = 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 + -10x)' equal to zero and attempt to solve:

Simplifying
1 + -10x = 0

Solving
1 + -10x = 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 + -10x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -10x = 0 + -1
-10x = 0 + -1

Combine like terms: 0 + -1 = -1
-10x = -1

Divide each side by '-10'.
x = 0.1

Simplifying
x = 0.1
Solution
x = {0, 0.1}

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