2x(3x-5)-2x=3x(x-1)

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Solution for 2x(3x-5)-2x=3x(x-1) equation:


Simplifying
2x(3x + -5) + -2x = 3x(x + -1)

Reorder the terms:
2x(-5 + 3x) + -2x = 3x(x + -1)
(-5 * 2x + 3x * 2x) + -2x = 3x(x + -1)
(-10x + 6x2) + -2x = 3x(x + -1)

Reorder the terms:
-10x + -2x + 6x2 = 3x(x + -1)

Combine like terms: -10x + -2x = -12x
-12x + 6x2 = 3x(x + -1)

Reorder the terms:
-12x + 6x2 = 3x(-1 + x)
-12x + 6x2 = (-1 * 3x + x * 3x)
-12x + 6x2 = (-3x + 3x2)

Solving
-12x + 6x2 = -3x + 3x2

Solving for variable 'x'.

Reorder the terms:
-12x + 3x + 6x2 + -3x2 = -3x + 3x2 + 3x + -3x2

Combine like terms: -12x + 3x = -9x
-9x + 6x2 + -3x2 = -3x + 3x2 + 3x + -3x2

Combine like terms: 6x2 + -3x2 = 3x2
-9x + 3x2 = -3x + 3x2 + 3x + -3x2

Reorder the terms:
-9x + 3x2 = -3x + 3x + 3x2 + -3x2

Combine like terms: -3x + 3x = 0
-9x + 3x2 = 0 + 3x2 + -3x2
-9x + 3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-9x + 3x2 = 0

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

Ignore the factor 3.

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 '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Simplifying
x = 3
Solution
x = {0, 3}

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