7x*2+3x-x^2=6x^2+3x

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Solution for 7x*2+3x-x^2=6x^2+3x equation: 


Simplifying
7x * 2 + 3x + -1x2 = 6x2 + 3x

Reorder the terms for easier multiplication:
7 * 2x + 3x + -1x2 = 6x2 + 3x

Multiply 7 * 2
14x + 3x + -1x2 = 6x2 + 3x

Combine like terms: 14x + 3x = 17x
17x + -1x2 = 6x2 + 3x

Reorder the terms:
17x + -1x2 = 3x + 6x2

Solving
17x + -1x2 = 3x + 6x2

Solving for variable 'x'.

Reorder the terms:
17x + -3x + -1x2 + -6x2 = 3x + 6x2 + -3x + -6x2

Combine like terms: 17x + -3x = 14x
14x + -1x2 + -6x2 = 3x + 6x2 + -3x + -6x2

Combine like terms: -1x2 + -6x2 = -7x2
14x + -7x2 = 3x + 6x2 + -3x + -6x2

Reorder the terms:
14x + -7x2 = 3x + -3x + 6x2 + -6x2

Combine like terms: 3x + -3x = 0
14x + -7x2 = 0 + 6x2 + -6x2
14x + -7x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
14x + -7x2 = 0

Factor out the Greatest Common Factor (GCF), '7x'.
7x(2 + -1x) = 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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0, 2}

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