-4x(x+10)=-3(x-2)

Solution for -4x(x+10)=-3(x-2) equation:

Simplifying
-4x(x + 10) = -3(x + -2)

Reorder the terms:
-4x(10 + x) = -3(x + -2)
(10 * -4x + x * -4x) = -3(x + -2)
(-40x + -4x2) = -3(x + -2)

Reorder the terms:
-40x + -4x2 = -3(-2 + x)
-40x + -4x2 = (-2 * -3 + x * -3)
-40x + -4x2 = (6 + -3x)

Solving
-40x + -4x2 = 6 + -3x

Solving for variable 'x'.

Reorder the terms:
-6 + -40x + 3x + -4x2 = 6 + -3x + -6 + 3x

Combine like terms: -40x + 3x = -37x
-6 + -37x + -4x2 = 6 + -3x + -6 + 3x

Reorder the terms:
-6 + -37x + -4x2 = 6 + -6 + -3x + 3x

Combine like terms: 6 + -6 = 0
-6 + -37x + -4x2 = 0 + -3x + 3x
-6 + -37x + -4x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-6 + -37x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 37x + 4x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + 37x + 4x2)' equal to zero and attempt to solve:

Simplifying
6 + 37x + 4x2 = 0

Solving
6 + 37x + 4x2 = 0

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

Divide each side by '4'.
1.5 + 9.25x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 9.25x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 9.25x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 9.25x + x2 = 0 + -1.5
9.25x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
9.25x + x2 = -1.5

The x term is 9.25x.  Take half its coefficient (4.625).
Square it (21.390625) and add it to both sides.

Add '21.390625' to each side of the equation.
9.25x + 21.390625 + x2 = -1.5 + 21.390625

Reorder the terms:
21.390625 + 9.25x + x2 = -1.5 + 21.390625

Combine like terms: -1.5 + 21.390625 = 19.890625
21.390625 + 9.25x + x2 = 19.890625

Factor a perfect square on the left side:
(x + 4.625)(x + 4.625) = 19.890625

Calculate the square root of the right side: 4.459890694

Break this problem into two subproblems by setting 
(x + 4.625) equal to 4.459890694 and -4.459890694.

Subproblem 1
x + 4.625 = 4.459890694

Simplifying
x + 4.625 = 4.459890694

Reorder the terms:
4.625 + x = 4.459890694

Solving
4.625 + x = 4.459890694

Solving for variable 'x'.

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

Add '-4.625' to each side of the equation.
4.625 + -4.625 + x = 4.459890694 + -4.625

Combine like terms: 4.625 + -4.625 = 0.000
0.000 + x = 4.459890694 + -4.625
x = 4.459890694 + -4.625

Combine like terms: 4.459890694 + -4.625 = -0.165109306
x = -0.165109306

Simplifying
x = -0.165109306

Subproblem 2
x + 4.625 = -4.459890694

Simplifying
x + 4.625 = -4.459890694

Reorder the terms:
4.625 + x = -4.459890694

Solving
4.625 + x = -4.459890694

Solving for variable 'x'.

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

Add '-4.625' to each side of the equation.
4.625 + -4.625 + x = -4.459890694 + -4.625

Combine like terms: 4.625 + -4.625 = 0.000
0.000 + x = -4.459890694 + -4.625
x = -4.459890694 + -4.625

Combine like terms: -4.459890694 + -4.625 = -9.084890694
x = -9.084890694

Simplifying
x = -9.084890694

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.165109306, -9.084890694}
Solution
x = {-0.165109306, -9.084890694}