4(x-7)=x(x+6)

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Solution for 4(x-7)=x(x+6) equation: 


Simplifying
4(x + -7) = x(x + 6)

Reorder the terms:
4(-7 + x) = x(x + 6)
(-7 * 4 + x * 4) = x(x + 6)
(-28 + 4x) = x(x + 6)

Reorder the terms:
-28 + 4x = x(6 + x)
-28 + 4x = (6 * x + x * x)
-28 + 4x = (6x + x2)

Solving
-28 + 4x = 6x + x2

Solving for variable 'x'.

Combine like terms: 4x + -6x = -2x
-28 + -2x + -1x2 = 6x + x2 + -6x + -1x2

Reorder the terms:
-28 + -2x + -1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
-28 + -2x + -1x2 = 0 + x2 + -1x2
-28 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-28 + -2x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(28 + 2x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(28 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
28 + 2x + x2 = 0

Solving
28 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + 2x + -28 + x2 = 0 + -28

Reorder the terms:
28 + -28 + 2x + x2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + 2x + x2 = 0 + -28
2x + x2 = 0 + -28

Combine like terms: 0 + -28 = -28
2x + x2 = -28

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -28 + 1

Reorder the terms:
1 + 2x + x2 = -28 + 1

Combine like terms: -28 + 1 = -27
1 + 2x + x2 = -27

Factor a perfect square on the left side:
(x + 1)(x + 1) = -27

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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