(4x+5)6x-5=

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Solution for (4x+5)6x-5= equation: 


Simplifying
(4x + 5) * 6x + -5 = 0

Reorder the terms:
(5 + 4x) * 6x + -5 = 0

Reorder the terms for easier multiplication:
6x(5 + 4x) + -5 = 0
(5 * 6x + 4x * 6x) + -5 = 0
(30x + 24x2) + -5 = 0

Reorder the terms:
-5 + 30x + 24x2 = 0

Solving
-5 + 30x + 24x2 = 0

Solving for variable 'x'.

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

Divide each side by '24'.
-0.2083333333 + 1.25x + x2 = 0

Move the constant term to the right:

Add '0.2083333333' to each side of the equation.
-0.2083333333 + 1.25x + 0.2083333333 + x2 = 0 + 0.2083333333

Reorder the terms:
-0.2083333333 + 0.2083333333 + 1.25x + x2 = 0 + 0.2083333333

Combine like terms: -0.2083333333 + 0.2083333333 = 0.0000000000
0.0000000000 + 1.25x + x2 = 0 + 0.2083333333
1.25x + x2 = 0 + 0.2083333333

Combine like terms: 0 + 0.2083333333 = 0.2083333333
1.25x + x2 = 0.2083333333

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 0.2083333333 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 0.2083333333 + 0.390625

Combine like terms: 0.2083333333 + 0.390625 = 0.5989583333
0.390625 + 1.25x + x2 = 0.5989583333

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 0.5989583333

Calculate the square root of the right side: 0.773923984

Break this problem into two subproblems by setting 
(x + 0.625) equal to 0.773923984 and -0.773923984.


Subproblem 1
x + 0.625 = 0.773923984

Simplifying
x + 0.625 = 0.773923984

Reorder the terms:
0.625 + x = 0.773923984

Solving
0.625 + x = 0.773923984

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = 0.773923984 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = 0.773923984 + -0.625
x = 0.773923984 + -0.625

Combine like terms: 0.773923984 + -0.625 = 0.148923984
x = 0.148923984

Simplifying
x = 0.148923984


Subproblem 2
x + 0.625 = -0.773923984

Simplifying
x + 0.625 = -0.773923984

Reorder the terms:
0.625 + x = -0.773923984

Solving
0.625 + x = -0.773923984

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = -0.773923984 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = -0.773923984 + -0.625
x = -0.773923984 + -0.625

Combine like terms: -0.773923984 + -0.625 = -1.398923984
x = -1.398923984

Simplifying
x = -1.398923984


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.148923984, -1.398923984}

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