7a-21=6a(a-2)

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Solution for 7a-21=6a(a-2) equation: 


Simplifying
7a + -21 = 6a(a + -2)

Reorder the terms:
-21 + 7a = 6a(a + -2)

Reorder the terms:
-21 + 7a = 6a(-2 + a)
-21 + 7a = (-2 * 6a + a * 6a)
-21 + 7a = (-12a + 6a2)

Solving
-21 + 7a = -12a + 6a2

Solving for variable 'a'.

Combine like terms: 7a + 12a = 19a
-21 + 19a + -6a2 = -12a + 6a2 + 12a + -6a2

Reorder the terms:
-21 + 19a + -6a2 = -12a + 12a + 6a2 + -6a2

Combine like terms: -12a + 12a = 0
-21 + 19a + -6a2 = 0 + 6a2 + -6a2
-21 + 19a + -6a2 = 6a2 + -6a2

Combine like terms: 6a2 + -6a2 = 0
-21 + 19a + -6a2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
3.5 + -3.166666667a + a2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + -3.166666667a + -3.5 + a2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + -3.166666667a + a2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + -3.166666667a + a2 = 0 + -3.5
-3.166666667a + a2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
-3.166666667a + a2 = -3.5

The a term is -3.166666667a.  Take half its coefficient (-1.583333334).
Square it (2.506944447) and add it to both sides.

Add '2.506944447' to each side of the equation.
-3.166666667a + 2.506944447 + a2 = -3.5 + 2.506944447

Reorder the terms:
2.506944447 + -3.166666667a + a2 = -3.5 + 2.506944447

Combine like terms: -3.5 + 2.506944447 = -0.993055553
2.506944447 + -3.166666667a + a2 = -0.993055553

Factor a perfect square on the left side:
(a + -1.583333334)(a + -1.583333334) = -0.993055553

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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