7x-3x(x+7)=67

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Solution for 7x-3x(x+7)=67 equation: 


Simplifying
7x + -3x(x + 7) = 67

Reorder the terms:
7x + -3x(7 + x) = 67
7x + (7 * -3x + x * -3x) = 67
7x + (-21x + -3x2) = 67

Combine like terms: 7x + -21x = -14x
-14x + -3x2 = 67

Solving
-14x + -3x2 = 67

Solving for variable 'x'.

Reorder the terms:
-67 + -14x + -3x2 = 67 + -67

Combine like terms: 67 + -67 = 0
-67 + -14x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(67 + 14x + 3x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(67 + 14x + 3x2)' equal to zero and attempt to solve:

Simplifying
67 + 14x + 3x2 = 0

Solving
67 + 14x + 3x2 = 0

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

Divide each side by '3'.
22.33333333 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '-22.33333333' to each side of the equation.
22.33333333 + 4.666666667x + -22.33333333 + x2 = 0 + -22.33333333

Reorder the terms:
22.33333333 + -22.33333333 + 4.666666667x + x2 = 0 + -22.33333333

Combine like terms: 22.33333333 + -22.33333333 = 0.00000000
0.00000000 + 4.666666667x + x2 = 0 + -22.33333333
4.666666667x + x2 = 0 + -22.33333333

Combine like terms: 0 + -22.33333333 = -22.33333333
4.666666667x + x2 = -22.33333333

The x term is 4.666666667x.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667x + 5.444444448 + x2 = -22.33333333 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = -22.33333333 + 5.444444448

Combine like terms: -22.33333333 + 5.444444448 = -16.888888882
5.444444448 + 4.666666667x + x2 = -16.888888882

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = -16.888888882

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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