-4(5-3x)+2x=(8x-3)(3x-10)

Solution for -4(5-3x)+2x=(8x-3)(3x-10) equation:

Simplifying
-4(5 + -3x) + 2x = (8x + -3)(3x + -10)
(5 * -4 + -3x * -4) + 2x = (8x + -3)(3x + -10)
(-20 + 12x) + 2x = (8x + -3)(3x + -10)

Combine like terms: 12x + 2x = 14x
-20 + 14x = (8x + -3)(3x + -10)

Reorder the terms:
-20 + 14x = (-3 + 8x)(3x + -10)

Reorder the terms:
-20 + 14x = (-3 + 8x)(-10 + 3x)

Multiply (-3 + 8x) * (-10 + 3x)
-20 + 14x = (-3(-10 + 3x) + 8x * (-10 + 3x))
-20 + 14x = ((-10 * -3 + 3x * -3) + 8x * (-10 + 3x))
-20 + 14x = ((30 + -9x) + 8x * (-10 + 3x))
-20 + 14x = (30 + -9x + (-10 * 8x + 3x * 8x))
-20 + 14x = (30 + -9x + (-80x + 24x2))

Combine like terms: -9x + -80x = -89x
-20 + 14x = (30 + -89x + 24x2)

Solving
-20 + 14x = 30 + -89x + 24x2

Solving for variable 'x'.

Reorder the terms:
-20 + -30 + 14x + 89x + -24x2 = 30 + -89x + 24x2 + -30 + 89x + -24x2

Combine like terms: -20 + -30 = -50
-50 + 14x + 89x + -24x2 = 30 + -89x + 24x2 + -30 + 89x + -24x2

Combine like terms: 14x + 89x = 103x
-50 + 103x + -24x2 = 30 + -89x + 24x2 + -30 + 89x + -24x2

Reorder the terms:
-50 + 103x + -24x2 = 30 + -30 + -89x + 89x + 24x2 + -24x2

Combine like terms: 30 + -30 = 0
-50 + 103x + -24x2 = 0 + -89x + 89x + 24x2 + -24x2
-50 + 103x + -24x2 = -89x + 89x + 24x2 + -24x2

Combine like terms: -89x + 89x = 0
-50 + 103x + -24x2 = 0 + 24x2 + -24x2
-50 + 103x + -24x2 = 24x2 + -24x2

Combine like terms: 24x2 + -24x2 = 0
-50 + 103x + -24x2 = 0

Begin completing the square.  Divide all terms by
-24 the coefficient of the squared term: 

Divide each side by '-24'.
2.083333333 + -4.291666667x + x2 = 0

Move the constant term to the right:

Add '-2.083333333' to each side of the equation.
2.083333333 + -4.291666667x + -2.083333333 + x2 = 0 + -2.083333333

Reorder the terms:
2.083333333 + -2.083333333 + -4.291666667x + x2 = 0 + -2.083333333

Combine like terms: 2.083333333 + -2.083333333 = 0.000000000
0.000000000 + -4.291666667x + x2 = 0 + -2.083333333
-4.291666667x + x2 = 0 + -2.083333333

Combine like terms: 0 + -2.083333333 = -2.083333333
-4.291666667x + x2 = -2.083333333

The x term is -4.291666667x.  Take half its coefficient (-2.145833334).
Square it (4.604600697) and add it to both sides.

Add '4.604600697' to each side of the equation.
-4.291666667x + 4.604600697 + x2 = -2.083333333 + 4.604600697

Reorder the terms:
4.604600697 + -4.291666667x + x2 = -2.083333333 + 4.604600697

Combine like terms: -2.083333333 + 4.604600697 = 2.521267364
4.604600697 + -4.291666667x + x2 = 2.521267364

Factor a perfect square on the left side:
(x + -2.145833334)(x + -2.145833334) = 2.521267364

Calculate the square root of the right side: 1.587849919

Break this problem into two subproblems by setting 
(x + -2.145833334) equal to 1.587849919 and -1.587849919.

Subproblem 1
x + -2.145833334 = 1.587849919

Simplifying
x + -2.145833334 = 1.587849919

Reorder the terms:
-2.145833334 + x = 1.587849919

Solving
-2.145833334 + x = 1.587849919

Solving for variable 'x'.

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

Add '2.145833334' to each side of the equation.
-2.145833334 + 2.145833334 + x = 1.587849919 + 2.145833334

Combine like terms: -2.145833334 + 2.145833334 = 0.000000000
0.000000000 + x = 1.587849919 + 2.145833334
x = 1.587849919 + 2.145833334

Combine like terms: 1.587849919 + 2.145833334 = 3.733683253
x = 3.733683253

Simplifying
x = 3.733683253

Subproblem 2
x + -2.145833334 = -1.587849919

Simplifying
x + -2.145833334 = -1.587849919

Reorder the terms:
-2.145833334 + x = -1.587849919

Solving
-2.145833334 + x = -1.587849919

Solving for variable 'x'.

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

Add '2.145833334' to each side of the equation.
-2.145833334 + 2.145833334 + x = -1.587849919 + 2.145833334

Combine like terms: -2.145833334 + 2.145833334 = 0.000000000
0.000000000 + x = -1.587849919 + 2.145833334
x = -1.587849919 + 2.145833334

Combine like terms: -1.587849919 + 2.145833334 = 0.557983415
x = 0.557983415

Simplifying
x = 0.557983415

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.733683253, 0.557983415}