0=-x^2+7x

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Solution for 0=-x^2+7x equation: 


Simplifying
0 = -1x2 + 7x

Reorder the terms:
0 = 7x + -1x2

Solving
0 = 7x + -1x2

Solving for variable 'x'.
Remove the zero:
-7x + x2 = 7x + -1x2 + -7x + x2

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

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

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

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

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

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

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7
Solution
x = {0, 7}

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