x(x-3)=4x-6x^2

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Solution for x(x-3)=4x-6x^2 equation: 


Simplifying
x(x + -3) = 4x + -6x2

Reorder the terms:
x(-3 + x) = 4x + -6x2
(-3 * x + x * x) = 4x + -6x2
(-3x + x2) = 4x + -6x2

Solving
-3x + x2 = 4x + -6x2

Solving for variable 'x'.

Reorder the terms:
-3x + -4x + x2 + 6x2 = 4x + -6x2 + -4x + 6x2

Combine like terms: -3x + -4x = -7x
-7x + x2 + 6x2 = 4x + -6x2 + -4x + 6x2

Combine like terms: x2 + 6x2 = 7x2
-7x + 7x2 = 4x + -6x2 + -4x + 6x2

Reorder the terms:
-7x + 7x2 = 4x + -4x + -6x2 + 6x2

Combine like terms: 4x + -4x = 0
-7x + 7x2 = 0 + -6x2 + 6x2
-7x + 7x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
-7x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), '7x'.
7x(-1 + x) = 0

Ignore the factor 7.

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 + 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
Solution
x = {0, 1}

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