4x(5x-3)=84

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Solution for 4x(5x-3)=84 equation: 


Simplifying
4x(5x + -3) = 84

Reorder the terms:
4x(-3 + 5x) = 84
(-3 * 4x + 5x * 4x) = 84
(-12x + 20x2) = 84

Solving
-12x + 20x2 = 84

Solving for variable 'x'.

Reorder the terms:
-84 + -12x + 20x2 = 84 + -84

Combine like terms: 84 + -84 = 0
-84 + -12x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-21 + -3x + 5x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-21 + -3x + 5x2)' equal to zero and attempt to solve:

Simplifying
-21 + -3x + 5x2 = 0

Solving
-21 + -3x + 5x2 = 0

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

Divide each side by '5'.
-4.2 + -0.6x + x2 = 0

Move the constant term to the right:

Add '4.2' to each side of the equation.
-4.2 + -0.6x + 4.2 + x2 = 0 + 4.2

Reorder the terms:
-4.2 + 4.2 + -0.6x + x2 = 0 + 4.2

Combine like terms: -4.2 + 4.2 = 0.0
0.0 + -0.6x + x2 = 0 + 4.2
-0.6x + x2 = 0 + 4.2

Combine like terms: 0 + 4.2 = 4.2
-0.6x + x2 = 4.2

The x term is -0.6x.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6x + 0.09 + x2 = 4.2 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = 4.2 + 0.09

Combine like terms: 4.2 + 0.09 = 4.29
0.09 + -0.6x + x2 = 4.29

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = 4.29

Calculate the square root of the right side: 2.071231518

Break this problem into two subproblems by setting 
(x + -0.3) equal to 2.071231518 and -2.071231518.


Subproblem 1
x + -0.3 = 2.071231518

Simplifying
x + -0.3 = 2.071231518

Reorder the terms:
-0.3 + x = 2.071231518

Solving
-0.3 + x = 2.071231518

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.3' to each side of the equation.
-0.3 + 0.3 + x = 2.071231518 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = 2.071231518 + 0.3
x = 2.071231518 + 0.3

Combine like terms: 2.071231518 + 0.3 = 2.371231518
x = 2.371231518

Simplifying
x = 2.371231518


Subproblem 2
x + -0.3 = -2.071231518

Simplifying
x + -0.3 = -2.071231518

Reorder the terms:
-0.3 + x = -2.071231518

Solving
-0.3 + x = -2.071231518

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.3' to each side of the equation.
-0.3 + 0.3 + x = -2.071231518 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = -2.071231518 + 0.3
x = -2.071231518 + 0.3

Combine like terms: -2.071231518 + 0.3 = -1.771231518
x = -1.771231518

Simplifying
x = -1.771231518


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.371231518, -1.771231518}
Solution
x = {2.371231518, -1.771231518}

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