5x(x-6)+21=6x+24

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Solution for 5x(x-6)+21=6x+24 equation:


Simplifying
5x(x + -6) + 21 = 6x + 24

Reorder the terms:
5x(-6 + x) + 21 = 6x + 24
(-6 * 5x + x * 5x) + 21 = 6x + 24
(-30x + 5x2) + 21 = 6x + 24

Reorder the terms:
21 + -30x + 5x2 = 6x + 24

Reorder the terms:
21 + -30x + 5x2 = 24 + 6x

Solving
21 + -30x + 5x2 = 24 + 6x

Solving for variable 'x'.

Reorder the terms:
21 + -24 + -30x + -6x + 5x2 = 24 + 6x + -24 + -6x

Combine like terms: 21 + -24 = -3
-3 + -30x + -6x + 5x2 = 24 + 6x + -24 + -6x

Combine like terms: -30x + -6x = -36x
-3 + -36x + 5x2 = 24 + 6x + -24 + -6x

Reorder the terms:
-3 + -36x + 5x2 = 24 + -24 + 6x + -6x

Combine like terms: 24 + -24 = 0
-3 + -36x + 5x2 = 0 + 6x + -6x
-3 + -36x + 5x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-3 + -36x + 5x2 = 0

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

Divide each side by '5'.
-0.6 + -7.2x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -7.2x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -7.2x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -7.2x + x2 = 0 + 0.6
-7.2x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-7.2x + x2 = 0.6

The x term is -7.2x.  Take half its coefficient (-3.6).
Square it (12.96) and add it to both sides.

Add '12.96' to each side of the equation.
-7.2x + 12.96 + x2 = 0.6 + 12.96

Reorder the terms:
12.96 + -7.2x + x2 = 0.6 + 12.96

Combine like terms: 0.6 + 12.96 = 13.56
12.96 + -7.2x + x2 = 13.56

Factor a perfect square on the left side:
(x + -3.6)(x + -3.6) = 13.56

Calculate the square root of the right side: 3.682390528

Break this problem into two subproblems by setting 
(x + -3.6) equal to 3.682390528 and -3.682390528.

Subproblem 1

x + -3.6 = 3.682390528 Simplifying x + -3.6 = 3.682390528 Reorder the terms: -3.6 + x = 3.682390528 Solving -3.6 + x = 3.682390528 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x = 3.682390528 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = 3.682390528 + 3.6 x = 3.682390528 + 3.6 Combine like terms: 3.682390528 + 3.6 = 7.282390528 x = 7.282390528 Simplifying x = 7.282390528

Subproblem 2

x + -3.6 = -3.682390528 Simplifying x + -3.6 = -3.682390528 Reorder the terms: -3.6 + x = -3.682390528 Solving -3.6 + x = -3.682390528 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x = -3.682390528 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = -3.682390528 + 3.6 x = -3.682390528 + 3.6 Combine like terms: -3.682390528 + 3.6 = -0.082390528 x = -0.082390528 Simplifying x = -0.082390528

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.282390528, -0.082390528}

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