1+1(3x+5)=4(3x+5)(4x-5)

Solution for 1+1(3x+5)=4(3x+5)(4x-5) equation:

Simplifying
1 + 1(3x + 5) = 4(3x + 5)(4x + -5)

Reorder the terms:
1 + 1(5 + 3x) = 4(3x + 5)(4x + -5)
1 + (5 * 1 + 3x * 1) = 4(3x + 5)(4x + -5)
1 + (5 + 3x) = 4(3x + 5)(4x + -5)

Combine like terms: 1 + 5 = 6
6 + 3x = 4(3x + 5)(4x + -5)

Reorder the terms:
6 + 3x = 4(5 + 3x)(4x + -5)

Reorder the terms:
6 + 3x = 4(5 + 3x)(-5 + 4x)

Multiply (5 + 3x) * (-5 + 4x)
6 + 3x = 4(5(-5 + 4x) + 3x * (-5 + 4x))
6 + 3x = 4((-5 * 5 + 4x * 5) + 3x * (-5 + 4x))
6 + 3x = 4((-25 + 20x) + 3x * (-5 + 4x))
6 + 3x = 4(-25 + 20x + (-5 * 3x + 4x * 3x))
6 + 3x = 4(-25 + 20x + (-15x + 12x2))

Combine like terms: 20x + -15x = 5x
6 + 3x = 4(-25 + 5x + 12x2)
6 + 3x = (-25 * 4 + 5x * 4 + 12x2 * 4)
6 + 3x = (-100 + 20x + 48x2)

Solving
6 + 3x = -100 + 20x + 48x2

Solving for variable 'x'.

Reorder the terms:
6 + 100 + 3x + -20x + -48x2 = -100 + 20x + 48x2 + 100 + -20x + -48x2

Combine like terms: 6 + 100 = 106
106 + 3x + -20x + -48x2 = -100 + 20x + 48x2 + 100 + -20x + -48x2

Combine like terms: 3x + -20x = -17x
106 + -17x + -48x2 = -100 + 20x + 48x2 + 100 + -20x + -48x2

Reorder the terms:
106 + -17x + -48x2 = -100 + 100 + 20x + -20x + 48x2 + -48x2

Combine like terms: -100 + 100 = 0
106 + -17x + -48x2 = 0 + 20x + -20x + 48x2 + -48x2
106 + -17x + -48x2 = 20x + -20x + 48x2 + -48x2

Combine like terms: 20x + -20x = 0
106 + -17x + -48x2 = 0 + 48x2 + -48x2
106 + -17x + -48x2 = 48x2 + -48x2

Combine like terms: 48x2 + -48x2 = 0
106 + -17x + -48x2 = 0

Begin completing the square.  Divide all terms by
-48 the coefficient of the squared term: 

Divide each side by '-48'.
-2.208333333 + 0.3541666667x + x2 = 0

Move the constant term to the right:

Add '2.208333333' to each side of the equation.
-2.208333333 + 0.3541666667x + 2.208333333 + x2 = 0 + 2.208333333

Reorder the terms:
-2.208333333 + 2.208333333 + 0.3541666667x + x2 = 0 + 2.208333333

Combine like terms: -2.208333333 + 2.208333333 = 0.000000000
0.000000000 + 0.3541666667x + x2 = 0 + 2.208333333
0.3541666667x + x2 = 0 + 2.208333333

Combine like terms: 0 + 2.208333333 = 2.208333333
0.3541666667x + x2 = 2.208333333

The x term is 0.3541666667x.  Take half its coefficient (0.1770833334).
Square it (0.03135850697) and add it to both sides.

Add '0.03135850697' to each side of the equation.
0.3541666667x + 0.03135850697 + x2 = 2.208333333 + 0.03135850697

Reorder the terms:
0.03135850697 + 0.3541666667x + x2 = 2.208333333 + 0.03135850697

Combine like terms: 2.208333333 + 0.03135850697 = 2.23969183997
0.03135850697 + 0.3541666667x + x2 = 2.23969183997

Factor a perfect square on the left side:
(x + 0.1770833334)(x + 0.1770833334) = 2.23969183997

Calculate the square root of the right side: 1.496560002

Break this problem into two subproblems by setting 
(x + 0.1770833334) equal to 1.496560002 and -1.496560002.

Subproblem 1
x + 0.1770833334 = 1.496560002

Simplifying
x + 0.1770833334 = 1.496560002

Reorder the terms:
0.1770833334 + x = 1.496560002

Solving
0.1770833334 + x = 1.496560002

Solving for variable 'x'.

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

Add '-0.1770833334' to each side of the equation.
0.1770833334 + -0.1770833334 + x = 1.496560002 + -0.1770833334

Combine like terms: 0.1770833334 + -0.1770833334 = 0.0000000000
0.0000000000 + x = 1.496560002 + -0.1770833334
x = 1.496560002 + -0.1770833334

Combine like terms: 1.496560002 + -0.1770833334 = 1.3194766686
x = 1.3194766686

Simplifying
x = 1.3194766686

Subproblem 2
x + 0.1770833334 = -1.496560002

Simplifying
x + 0.1770833334 = -1.496560002

Reorder the terms:
0.1770833334 + x = -1.496560002

Solving
0.1770833334 + x = -1.496560002

Solving for variable 'x'.

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

Add '-0.1770833334' to each side of the equation.
0.1770833334 + -0.1770833334 + x = -1.496560002 + -0.1770833334

Combine like terms: 0.1770833334 + -0.1770833334 = 0.0000000000
0.0000000000 + x = -1.496560002 + -0.1770833334
x = -1.496560002 + -0.1770833334

Combine like terms: -1.496560002 + -0.1770833334 = -1.6736433354
x = -1.6736433354

Simplifying
x = -1.6736433354

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.3194766686, -1.6736433354}