5(2+6)=-4(-5-2x)3x

Solution for 5(2+6)=-4(-5-2x)3x equation:

Simplifying
5(2 + 6) = -4(-5 + -2x) * 3x

Combine like terms: 2 + 6 = 8
5(8) = -4(-5 + -2x) * 3x

Multiply 5 * 8
40 = -4(-5 + -2x) * 3x

Reorder the terms for easier multiplication:
40 = -4 * 3x(-5 + -2x)

Multiply -4 * 3
40 = -12x(-5 + -2x)
40 = (-5 * -12x + -2x * -12x)
40 = (60x + 24x2)

Solving
40 = 60x + 24x2

Solving for variable 'x'.

Reorder the terms:
40 + -60x + -24x2 = 60x + -60x + 24x2 + -24x2

Combine like terms: 60x + -60x = 0
40 + -60x + -24x2 = 0 + 24x2 + -24x2
40 + -60x + -24x2 = 24x2 + -24x2

Combine like terms: 24x2 + -24x2 = 0
40 + -60x + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(10 + -15x + -6x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(10 + -15x + -6x2)' equal to zero and attempt to solve:

Simplifying
10 + -15x + -6x2 = 0

Solving
10 + -15x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-1.666666667 + 2.5x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 2.5x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 2.5x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 2.5x + x2 = 0 + 1.666666667
2.5x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
2.5x + x2 = 1.666666667

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 1.666666667 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 1.666666667 + 1.5625

Combine like terms: 1.666666667 + 1.5625 = 3.229166667
1.5625 + 2.5x + x2 = 3.229166667

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 3.229166667

Calculate the square root of the right side: 1.796988221

Break this problem into two subproblems by setting 
(x + 1.25) equal to 1.796988221 and -1.796988221.

Subproblem 1
x + 1.25 = 1.796988221

Simplifying
x + 1.25 = 1.796988221

Reorder the terms:
1.25 + x = 1.796988221

Solving
1.25 + x = 1.796988221

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 1.796988221 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 1.796988221 + -1.25
x = 1.796988221 + -1.25

Combine like terms: 1.796988221 + -1.25 = 0.546988221
x = 0.546988221

Simplifying
x = 0.546988221

Subproblem 2
x + 1.25 = -1.796988221

Simplifying
x + 1.25 = -1.796988221

Reorder the terms:
1.25 + x = -1.796988221

Solving
1.25 + x = -1.796988221

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -1.796988221 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -1.796988221 + -1.25
x = -1.796988221 + -1.25

Combine like terms: -1.796988221 + -1.25 = -3.046988221
x = -3.046988221

Simplifying
x = -3.046988221

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.546988221, -3.046988221}
Solution
x = {0.546988221, -3.046988221}