x(4x-7)=5x-(x+21)

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Solution for x(4x-7)=5x-(x+21) equation: 


Simplifying
x(4x + -7) = 5x + -1(x + 21)

Reorder the terms:
x(-7 + 4x) = 5x + -1(x + 21)
(-7 * x + 4x * x) = 5x + -1(x + 21)
(-7x + 4x2) = 5x + -1(x + 21)

Reorder the terms:
-7x + 4x2 = 5x + -1(21 + x)
-7x + 4x2 = 5x + (21 * -1 + x * -1)
-7x + 4x2 = 5x + (-21 + -1x)

Reorder the terms:
-7x + 4x2 = -21 + 5x + -1x

Combine like terms: 5x + -1x = 4x
-7x + 4x2 = -21 + 4x

Solving
-7x + 4x2 = -21 + 4x

Solving for variable 'x'.

Reorder the terms:
21 + -7x + -4x + 4x2 = -21 + 4x + 21 + -4x

Combine like terms: -7x + -4x = -11x
21 + -11x + 4x2 = -21 + 4x + 21 + -4x

Reorder the terms:
21 + -11x + 4x2 = -21 + 21 + 4x + -4x

Combine like terms: -21 + 21 = 0
21 + -11x + 4x2 = 0 + 4x + -4x
21 + -11x + 4x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
21 + -11x + 4x2 = 0

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

Divide each side by '4'.
5.25 + -2.75x + x2 = 0

Move the constant term to the right:

Add '-5.25' to each side of the equation.
5.25 + -2.75x + -5.25 + x2 = 0 + -5.25

Reorder the terms:
5.25 + -5.25 + -2.75x + x2 = 0 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + -2.75x + x2 = 0 + -5.25
-2.75x + x2 = 0 + -5.25

Combine like terms: 0 + -5.25 = -5.25
-2.75x + x2 = -5.25

The x term is -2.75x.  Take half its coefficient (-1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
-2.75x + 1.890625 + x2 = -5.25 + 1.890625

Reorder the terms:
1.890625 + -2.75x + x2 = -5.25 + 1.890625

Combine like terms: -5.25 + 1.890625 = -3.359375
1.890625 + -2.75x + x2 = -3.359375

Factor a perfect square on the left side:
(x + -1.375)(x + -1.375) = -3.359375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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