2x(x-3)=7x^2-7x

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Solution for 2x(x-3)=7x^2-7x equation: 


Simplifying
2x(x + -3) = 7x2 + -7x

Reorder the terms:
2x(-3 + x) = 7x2 + -7x
(-3 * 2x + x * 2x) = 7x2 + -7x
(-6x + 2x2) = 7x2 + -7x

Reorder the terms:
-6x + 2x2 = -7x + 7x2

Solving
-6x + 2x2 = -7x + 7x2

Solving for variable 'x'.

Reorder the terms:
-6x + 7x + 2x2 + -7x2 = -7x + 7x2 + 7x + -7x2

Combine like terms: -6x + 7x = 1x
1x + 2x2 + -7x2 = -7x + 7x2 + 7x + -7x2

Combine like terms: 2x2 + -7x2 = -5x2
1x + -5x2 = -7x + 7x2 + 7x + -7x2

Reorder the terms:
1x + -5x2 = -7x + 7x + 7x2 + -7x2

Combine like terms: -7x + 7x = 0
1x + -5x2 = 0 + 7x2 + -7x2
1x + -5x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
1x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -5x) = 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 + -5x)' equal to zero and attempt to solve:

Simplifying
1 + -5x = 0

Solving
1 + -5x = 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 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2
Solution
x = {0, 0.2}

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