3a-4=a(a-3)

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Solution for 3a-4=a(a-3) equation:


Simplifying
3a + -4 = a(a + -3)

Reorder the terms:
-4 + 3a = a(a + -3)

Reorder the terms:
-4 + 3a = a(-3 + a)
-4 + 3a = (-3 * a + a * a)
-4 + 3a = (-3a + a2)

Solving
-4 + 3a = -3a + a2

Solving for variable 'a'.

Combine like terms: 3a + 3a = 6a
-4 + 6a + -1a2 = -3a + a2 + 3a + -1a2

Reorder the terms:
-4 + 6a + -1a2 = -3a + 3a + a2 + -1a2

Combine like terms: -3a + 3a = 0
-4 + 6a + -1a2 = 0 + a2 + -1a2
-4 + 6a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-4 + 6a + -1a2 = 0

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

Divide each side by '-1'.
4 + -6a + a2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -6a + -4 + a2 = 0 + -4

Reorder the terms:
4 + -4 + -6a + a2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -6a + a2 = 0 + -4
-6a + a2 = 0 + -4

Combine like terms: 0 + -4 = -4
-6a + a2 = -4

The a term is -6a.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6a + 9 + a2 = -4 + 9

Reorder the terms:
9 + -6a + a2 = -4 + 9

Combine like terms: -4 + 9 = 5
9 + -6a + a2 = 5

Factor a perfect square on the left side:
(a + -3)(a + -3) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(a + -3) equal to 2.236067978 and -2.236067978.

Subproblem 1

a + -3 = 2.236067978 Simplifying a + -3 = 2.236067978 Reorder the terms: -3 + a = 2.236067978 Solving -3 + a = 2.236067978 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = 2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + a = 2.236067978 + 3 a = 2.236067978 + 3 Combine like terms: 2.236067978 + 3 = 5.236067978 a = 5.236067978 Simplifying a = 5.236067978

Subproblem 2

a + -3 = -2.236067978 Simplifying a + -3 = -2.236067978 Reorder the terms: -3 + a = -2.236067978 Solving -3 + a = -2.236067978 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = -2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + a = -2.236067978 + 3 a = -2.236067978 + 3 Combine like terms: -2.236067978 + 3 = 0.763932022 a = 0.763932022 Simplifying a = 0.763932022

Solution

The solution to the problem is based on the solutions from the subproblems. a = {5.236067978, 0.763932022}

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