(4x-3)x=144

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Solution for (4x-3)x=144 equation:


Simplifying
(4x + -3) * x = 144

Reorder the terms:
(-3 + 4x) * x = 144

Reorder the terms for easier multiplication:
x(-3 + 4x) = 144
(-3 * x + 4x * x) = 144
(-3x + 4x2) = 144

Solving
-3x + 4x2 = 144

Solving for variable 'x'.

Reorder the terms:
-144 + -3x + 4x2 = 144 + -144

Combine like terms: 144 + -144 = 0
-144 + -3x + 4x2 = 0

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

Divide each side by '4'.
-36 + -0.75x + x2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -0.75x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + -0.75x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -0.75x + x2 = 0 + 36
-0.75x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
-0.75x + x2 = 36

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 36 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 36 + 0.140625

Combine like terms: 36 + 0.140625 = 36.140625
0.140625 + -0.75x + x2 = 36.140625

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 36.140625

Calculate the square root of the right side: 6.011707328

Break this problem into two subproblems by setting 
(x + -0.375) equal to 6.011707328 and -6.011707328.


Subproblem 1
x + -0.375 = 6.011707328

Simplifying
x + -0.375 = 6.011707328

Reorder the terms:
-0.375 + x = 6.011707328

Solving
-0.375 + x = 6.011707328

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = 6.011707328 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 6.011707328 + 0.375
x = 6.011707328 + 0.375

Combine like terms: 6.011707328 + 0.375 = 6.386707328
x = 6.386707328

Simplifying
x = 6.386707328


Subproblem 2
x + -0.375 = -6.011707328

Simplifying
x + -0.375 = -6.011707328

Reorder the terms:
-0.375 + x = -6.011707328

Solving
-0.375 + x = -6.011707328

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = -6.011707328 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -6.011707328 + 0.375
x = -6.011707328 + 0.375

Combine like terms: -6.011707328 + 0.375 = -5.636707328
x = -5.636707328

Simplifying
x = -5.636707328


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.386707328, -5.636707328}

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