x(7-2x)=60-x

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Solution for x(7-2x)=60-x equation: 


Simplifying
x(7 + -2x) = 60 + -1x
(7 * x + -2x * x) = 60 + -1x
(7x + -2x2) = 60 + -1x

Solving
7x + -2x2 = 60 + -1x

Solving for variable 'x'.

Reorder the terms:
-60 + 7x + x + -2x2 = 60 + -1x + -60 + x

Combine like terms: 7x + x = 8x
-60 + 8x + -2x2 = 60 + -1x + -60 + x

Reorder the terms:
-60 + 8x + -2x2 = 60 + -60 + -1x + x

Combine like terms: 60 + -60 = 0
-60 + 8x + -2x2 = 0 + -1x + x
-60 + 8x + -2x2 = -1x + x

Combine like terms: -1x + x = 0
-60 + 8x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + 4x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-30 + 4x + -1x2)' equal to zero and attempt to solve:

Simplifying
-30 + 4x + -1x2 = 0

Solving
-30 + 4x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
30 + -4x + x2 = 0

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + -4x + -30 + x2 = 0 + -30

Reorder the terms:
30 + -30 + -4x + x2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -4x + x2 = 0 + -30
-4x + x2 = 0 + -30

Combine like terms: 0 + -30 = -30
-4x + x2 = -30

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -30 + 4

Reorder the terms:
4 + -4x + x2 = -30 + 4

Combine like terms: -30 + 4 = -26
4 + -4x + x2 = -26

Factor a perfect square on the left side:
(x + -2)(x + -2) = -26

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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