3(4x-2)(7x+10)=5

Solution for 3(4x-2)(7x+10)=5 equation:

Simplifying
3(4x + -2)(7x + 10) = 5

Reorder the terms:
3(-2 + 4x)(7x + 10) = 5

Reorder the terms:
3(-2 + 4x)(10 + 7x) = 5

Multiply (-2 + 4x) * (10 + 7x)
3(-2(10 + 7x) + 4x * (10 + 7x)) = 5
3((10 * -2 + 7x * -2) + 4x * (10 + 7x)) = 5
3((-20 + -14x) + 4x * (10 + 7x)) = 5
3(-20 + -14x + (10 * 4x + 7x * 4x)) = 5
3(-20 + -14x + (40x + 28x2)) = 5

Combine like terms: -14x + 40x = 26x
3(-20 + 26x + 28x2) = 5
(-20 * 3 + 26x * 3 + 28x2 * 3) = 5
(-60 + 78x + 84x2) = 5

Solving
-60 + 78x + 84x2 = 5

Solving for variable 'x'.

Reorder the terms:
-60 + -5 + 78x + 84x2 = 5 + -5

Combine like terms: -60 + -5 = -65
-65 + 78x + 84x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-65 + 78x + 84x2 = 0

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

Divide each side by '84'.
-0.7738095238 + 0.9285714286x + x2 = 0

Move the constant term to the right:

Add '0.7738095238' to each side of the equation.
-0.7738095238 + 0.9285714286x + 0.7738095238 + x2 = 0 + 0.7738095238

Reorder the terms:
-0.7738095238 + 0.7738095238 + 0.9285714286x + x2 = 0 + 0.7738095238

Combine like terms: -0.7738095238 + 0.7738095238 = 0.0000000000
0.0000000000 + 0.9285714286x + x2 = 0 + 0.7738095238
0.9285714286x + x2 = 0 + 0.7738095238

Combine like terms: 0 + 0.7738095238 = 0.7738095238
0.9285714286x + x2 = 0.7738095238

The x term is 0.9285714286x.  Take half its coefficient (0.4642857143).
Square it (0.2155612245) and add it to both sides.

Add '0.2155612245' to each side of the equation.
0.9285714286x + 0.2155612245 + x2 = 0.7738095238 + 0.2155612245

Reorder the terms:
0.2155612245 + 0.9285714286x + x2 = 0.7738095238 + 0.2155612245

Combine like terms: 0.7738095238 + 0.2155612245 = 0.9893707483
0.2155612245 + 0.9285714286x + x2 = 0.9893707483

Factor a perfect square on the left side:
(x + 0.4642857143)(x + 0.4642857143) = 0.9893707483

Calculate the square root of the right side: 0.994671176

Break this problem into two subproblems by setting 
(x + 0.4642857143) equal to 0.994671176 and -0.994671176.

Subproblem 1
x + 0.4642857143 = 0.994671176

Simplifying
x + 0.4642857143 = 0.994671176

Reorder the terms:
0.4642857143 + x = 0.994671176

Solving
0.4642857143 + x = 0.994671176

Solving for variable 'x'.

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

Add '-0.4642857143' to each side of the equation.
0.4642857143 + -0.4642857143 + x = 0.994671176 + -0.4642857143

Combine like terms: 0.4642857143 + -0.4642857143 = 0.0000000000
0.0000000000 + x = 0.994671176 + -0.4642857143
x = 0.994671176 + -0.4642857143

Combine like terms: 0.994671176 + -0.4642857143 = 0.5303854617
x = 0.5303854617

Simplifying
x = 0.5303854617

Subproblem 2
x + 0.4642857143 = -0.994671176

Simplifying
x + 0.4642857143 = -0.994671176

Reorder the terms:
0.4642857143 + x = -0.994671176

Solving
0.4642857143 + x = -0.994671176

Solving for variable 'x'.

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

Add '-0.4642857143' to each side of the equation.
0.4642857143 + -0.4642857143 + x = -0.994671176 + -0.4642857143

Combine like terms: 0.4642857143 + -0.4642857143 = 0.0000000000
0.0000000000 + x = -0.994671176 + -0.4642857143
x = -0.994671176 + -0.4642857143

Combine like terms: -0.994671176 + -0.4642857143 = -1.4589568903
x = -1.4589568903

Simplifying
x = -1.4589568903

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5303854617, -1.4589568903}