5(5x+6)3(8x-8)+43=

Solution for 5(5x+6)3(8x-8)+43= equation:

Simplifying
5(5x + 6) * 3(8x + -8) + 43 = 0

Reorder the terms:
5(6 + 5x) * 3(8x + -8) + 43 = 0

Reorder the terms:
5(6 + 5x) * 3(-8 + 8x) + 43 = 0

Reorder the terms for easier multiplication:
5 * 3(6 + 5x)(-8 + 8x) + 43 = 0

Multiply 5 * 3
15(6 + 5x)(-8 + 8x) + 43 = 0

Multiply (6 + 5x) * (-8 + 8x)
15(6(-8 + 8x) + 5x * (-8 + 8x)) + 43 = 0
15((-8 * 6 + 8x * 6) + 5x * (-8 + 8x)) + 43 = 0
15((-48 + 48x) + 5x * (-8 + 8x)) + 43 = 0
15(-48 + 48x + (-8 * 5x + 8x * 5x)) + 43 = 0
15(-48 + 48x + (-40x + 40x2)) + 43 = 0

Combine like terms: 48x + -40x = 8x
15(-48 + 8x + 40x2) + 43 = 0
(-48 * 15 + 8x * 15 + 40x2 * 15) + 43 = 0
(-720 + 120x + 600x2) + 43 = 0

Reorder the terms:
-720 + 43 + 120x + 600x2 = 0

Combine like terms: -720 + 43 = -677
-677 + 120x + 600x2 = 0

Solving
-677 + 120x + 600x2 = 0

Solving for variable 'x'.

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

Divide each side by '600'.
-1.128333333 + 0.2x + x2 = 0.00

Move the constant term to the right:

Add '1.128333333' to each side of the equation.
-1.128333333 + 0.2x + 1.128333333 + x2 = 0.00 + 1.128333333

Reorder the terms:
-1.128333333 + 1.128333333 + 0.2x + x2 = 0.00 + 1.128333333

Combine like terms: -1.128333333 + 1.128333333 = 0.000000000
0.000000000 + 0.2x + x2 = 0.00 + 1.128333333
0.2x + x2 = 0.00 + 1.128333333

Combine like terms: 0.00 + 1.128333333 = 1.128333333
0.2x + x2 = 1.128333333

The x term is 0.2x.  Take half its coefficient (0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
0.2x + 0.01 + x2 = 1.128333333 + 0.01

Reorder the terms:
0.01 + 0.2x + x2 = 1.128333333 + 0.01

Combine like terms: 1.128333333 + 0.01 = 1.138333333
0.01 + 0.2x + x2 = 1.138333333

Factor a perfect square on the left side:
(x + 0.1)(x + 0.1) = 1.138333333

Calculate the square root of the right side: 1.066927051

Break this problem into two subproblems by setting 
(x + 0.1) equal to 1.066927051 and -1.066927051.

Subproblem 1
x + 0.1 = 1.066927051

Simplifying
x + 0.1 = 1.066927051

Reorder the terms:
0.1 + x = 1.066927051

Solving
0.1 + x = 1.066927051

Solving for variable 'x'.

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

Add '-0.1' to each side of the equation.
0.1 + -0.1 + x = 1.066927051 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + x = 1.066927051 + -0.1
x = 1.066927051 + -0.1

Combine like terms: 1.066927051 + -0.1 = 0.966927051
x = 0.966927051

Simplifying
x = 0.966927051

Subproblem 2
x + 0.1 = -1.066927051

Simplifying
x + 0.1 = -1.066927051

Reorder the terms:
0.1 + x = -1.066927051

Solving
0.1 + x = -1.066927051

Solving for variable 'x'.

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

Add '-0.1' to each side of the equation.
0.1 + -0.1 + x = -1.066927051 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + x = -1.066927051 + -0.1
x = -1.066927051 + -0.1

Combine like terms: -1.066927051 + -0.1 = -1.166927051
x = -1.166927051

Simplifying
x = -1.166927051

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.966927051, -1.166927051}