3(x-2)5(2x+1)=3

Solution for 3(x-2)5(2x+1)=3 equation:

Simplifying
3(x + -2) * 5(2x + 1) = 3

Reorder the terms:
3(-2 + x) * 5(2x + 1) = 3

Reorder the terms:
3(-2 + x) * 5(1 + 2x) = 3

Reorder the terms for easier multiplication:
3 * 5(-2 + x)(1 + 2x) = 3

Multiply 3 * 5
15(-2 + x)(1 + 2x) = 3

Multiply (-2 + x) * (1 + 2x)
15(-2(1 + 2x) + x(1 + 2x)) = 3
15((1 * -2 + 2x * -2) + x(1 + 2x)) = 3
15((-2 + -4x) + x(1 + 2x)) = 3
15(-2 + -4x + (1 * x + 2x * x)) = 3
15(-2 + -4x + (1x + 2x2)) = 3

Combine like terms: -4x + 1x = -3x
15(-2 + -3x + 2x2) = 3
(-2 * 15 + -3x * 15 + 2x2 * 15) = 3
(-30 + -45x + 30x2) = 3

Solving
-30 + -45x + 30x2 = 3

Solving for variable 'x'.

Reorder the terms:
-30 + -3 + -45x + 30x2 = 3 + -3

Combine like terms: -30 + -3 = -33
-33 + -45x + 30x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-33 + -45x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-11 + -15x + 10x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-11 + -15x + 10x2)' equal to zero and attempt to solve:

Simplifying
-11 + -15x + 10x2 = 0

Solving
-11 + -15x + 10x2 = 0

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

Divide each side by '10'.
-1.1 + -1.5x + x2 = 0.0

Move the constant term to the right:

Add '1.1' to each side of the equation.
-1.1 + -1.5x + 1.1 + x2 = 0.0 + 1.1

Reorder the terms:
-1.1 + 1.1 + -1.5x + x2 = 0.0 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + -1.5x + x2 = 0.0 + 1.1
-1.5x + x2 = 0.0 + 1.1

Combine like terms: 0.0 + 1.1 = 1.1
-1.5x + x2 = 1.1

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 1.1 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 1.1 + 0.5625

Combine like terms: 1.1 + 0.5625 = 1.6625
0.5625 + -1.5x + x2 = 1.6625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 1.6625

Calculate the square root of the right side: 1.289379696

Break this problem into two subproblems by setting 
(x + -0.75) equal to 1.289379696 and -1.289379696.

Subproblem 1
x + -0.75 = 1.289379696

Simplifying
x + -0.75 = 1.289379696

Reorder the terms:
-0.75 + x = 1.289379696

Solving
-0.75 + x = 1.289379696

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = 1.289379696 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 1.289379696 + 0.75
x = 1.289379696 + 0.75

Combine like terms: 1.289379696 + 0.75 = 2.039379696
x = 2.039379696

Simplifying
x = 2.039379696

Subproblem 2
x + -0.75 = -1.289379696

Simplifying
x + -0.75 = -1.289379696

Reorder the terms:
-0.75 + x = -1.289379696

Solving
-0.75 + x = -1.289379696

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = -1.289379696 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -1.289379696 + 0.75
x = -1.289379696 + 0.75

Combine like terms: -1.289379696 + 0.75 = -0.539379696
x = -0.539379696

Simplifying
x = -0.539379696

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.039379696, -0.539379696}
Solution
x = {2.039379696, -0.539379696}