4(5+3x)4(4+5x)=15

Solution for 4(5+3x)4(4+5x)=15 equation:

Simplifying
4(5 + 3x) * 4(4 + 5x) = 15

Reorder the terms for easier multiplication:
4 * 4(5 + 3x)(4 + 5x) = 15

Multiply 4 * 4
16(5 + 3x)(4 + 5x) = 15

Multiply (5 + 3x) * (4 + 5x)
16(5(4 + 5x) + 3x * (4 + 5x)) = 15
16((4 * 5 + 5x * 5) + 3x * (4 + 5x)) = 15
16((20 + 25x) + 3x * (4 + 5x)) = 15
16(20 + 25x + (4 * 3x + 5x * 3x)) = 15
16(20 + 25x + (12x + 15x2)) = 15

Combine like terms: 25x + 12x = 37x
16(20 + 37x + 15x2) = 15
(20 * 16 + 37x * 16 + 15x2 * 16) = 15
(320 + 592x + 240x2) = 15

Solving
320 + 592x + 240x2 = 15

Solving for variable 'x'.

Reorder the terms:
320 + -15 + 592x + 240x2 = 15 + -15

Combine like terms: 320 + -15 = 305
305 + 592x + 240x2 = 15 + -15

Combine like terms: 15 + -15 = 0
305 + 592x + 240x2 = 0

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

Divide each side by '240'.
1.270833333 + 2.466666667x + x2 = 0.0

Move the constant term to the right:

Add '-1.270833333' to each side of the equation.
1.270833333 + 2.466666667x + -1.270833333 + x2 = 0.0 + -1.270833333

Reorder the terms:
1.270833333 + -1.270833333 + 2.466666667x + x2 = 0.0 + -1.270833333

Combine like terms: 1.270833333 + -1.270833333 = 0.000000000
0.000000000 + 2.466666667x + x2 = 0.0 + -1.270833333
2.466666667x + x2 = 0.0 + -1.270833333

Combine like terms: 0.0 + -1.270833333 = -1.270833333
2.466666667x + x2 = -1.270833333

The x term is 2.466666667x.  Take half its coefficient (1.233333334).
Square it (1.521111113) and add it to both sides.

Add '1.521111113' to each side of the equation.
2.466666667x + 1.521111113 + x2 = -1.270833333 + 1.521111113

Reorder the terms:
1.521111113 + 2.466666667x + x2 = -1.270833333 + 1.521111113

Combine like terms: -1.270833333 + 1.521111113 = 0.25027778
1.521111113 + 2.466666667x + x2 = 0.25027778

Factor a perfect square on the left side:
(x + 1.233333334)(x + 1.233333334) = 0.25027778

Calculate the square root of the right side: 0.500277703

Break this problem into two subproblems by setting 
(x + 1.233333334) equal to 0.500277703 and -0.500277703.

Subproblem 1
x + 1.233333334 = 0.500277703

Simplifying
x + 1.233333334 = 0.500277703

Reorder the terms:
1.233333334 + x = 0.500277703

Solving
1.233333334 + x = 0.500277703

Solving for variable 'x'.

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

Add '-1.233333334' to each side of the equation.
1.233333334 + -1.233333334 + x = 0.500277703 + -1.233333334

Combine like terms: 1.233333334 + -1.233333334 = 0.000000000
0.000000000 + x = 0.500277703 + -1.233333334
x = 0.500277703 + -1.233333334

Combine like terms: 0.500277703 + -1.233333334 = -0.733055631
x = -0.733055631

Simplifying
x = -0.733055631

Subproblem 2
x + 1.233333334 = -0.500277703

Simplifying
x + 1.233333334 = -0.500277703

Reorder the terms:
1.233333334 + x = -0.500277703

Solving
1.233333334 + x = -0.500277703

Solving for variable 'x'.

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

Add '-1.233333334' to each side of the equation.
1.233333334 + -1.233333334 + x = -0.500277703 + -1.233333334

Combine like terms: 1.233333334 + -1.233333334 = 0.000000000
0.000000000 + x = -0.500277703 + -1.233333334
x = -0.500277703 + -1.233333334

Combine like terms: -0.500277703 + -1.233333334 = -1.733611037
x = -1.733611037

Simplifying
x = -1.733611037

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.733055631, -1.733611037}