-(2x-3)*(5x-1)-2*(3-2x)*(4-6x)=34x^2+68x-28

Solution for -(2x-3)*(5x-1)-2*(3-2x)*(4-6x)=34x^2+68x-28 equation:

Simplifying
-1(2x + -3)(5x + -1) + -2(3 + -2x)(4 + -6x) = 34x2 + 68x + -28

Reorder the terms:
-1(-3 + 2x)(5x + -1) + -2(3 + -2x)(4 + -6x) = 34x2 + 68x + -28

Reorder the terms:
-1(-3 + 2x)(-1 + 5x) + -2(3 + -2x)(4 + -6x) = 34x2 + 68x + -28

Multiply (-3 + 2x) * (-1 + 5x)
-1(-3(-1 + 5x) + 2x * (-1 + 5x)) + -2(3 + -2x)(4 + -6x) = 34x2 + 68x + -28
-1((-1 * -3 + 5x * -3) + 2x * (-1 + 5x)) + -2(3 + -2x)(4 + -6x) = 34x2 + 68x + -28
-1((3 + -15x) + 2x * (-1 + 5x)) + -2(3 + -2x)(4 + -6x) = 34x2 + 68x + -28
-1(3 + -15x + (-1 * 2x + 5x * 2x)) + -2(3 + -2x)(4 + -6x) = 34x2 + 68x + -28
-1(3 + -15x + (-2x + 10x2)) + -2(3 + -2x)(4 + -6x) = 34x2 + 68x + -28

Combine like terms: -15x + -2x = -17x
-1(3 + -17x + 10x2) + -2(3 + -2x)(4 + -6x) = 34x2 + 68x + -28
(3 * -1 + -17x * -1 + 10x2 * -1) + -2(3 + -2x)(4 + -6x) = 34x2 + 68x + -28
(-3 + 17x + -10x2) + -2(3 + -2x)(4 + -6x) = 34x2 + 68x + -28

Multiply (3 + -2x) * (4 + -6x)
-3 + 17x + -10x2 + -2(3(4 + -6x) + -2x * (4 + -6x)) = 34x2 + 68x + -28
-3 + 17x + -10x2 + -2((4 * 3 + -6x * 3) + -2x * (4 + -6x)) = 34x2 + 68x + -28
-3 + 17x + -10x2 + -2((12 + -18x) + -2x * (4 + -6x)) = 34x2 + 68x + -28
-3 + 17x + -10x2 + -2(12 + -18x + (4 * -2x + -6x * -2x)) = 34x2 + 68x + -28
-3 + 17x + -10x2 + -2(12 + -18x + (-8x + 12x2)) = 34x2 + 68x + -28

Combine like terms: -18x + -8x = -26x
-3 + 17x + -10x2 + -2(12 + -26x + 12x2) = 34x2 + 68x + -28
-3 + 17x + -10x2 + (12 * -2 + -26x * -2 + 12x2 * -2) = 34x2 + 68x + -28
-3 + 17x + -10x2 + (-24 + 52x + -24x2) = 34x2 + 68x + -28

Reorder the terms:
-3 + -24 + 17x + 52x + -10x2 + -24x2 = 34x2 + 68x + -28

Combine like terms: -3 + -24 = -27
-27 + 17x + 52x + -10x2 + -24x2 = 34x2 + 68x + -28

Combine like terms: 17x + 52x = 69x
-27 + 69x + -10x2 + -24x2 = 34x2 + 68x + -28

Combine like terms: -10x2 + -24x2 = -34x2
-27 + 69x + -34x2 = 34x2 + 68x + -28

Reorder the terms:
-27 + 69x + -34x2 = -28 + 68x + 34x2

Solving
-27 + 69x + -34x2 = -28 + 68x + 34x2

Solving for variable 'x'.

Reorder the terms:
-27 + 28 + 69x + -68x + -34x2 + -34x2 = -28 + 68x + 34x2 + 28 + -68x + -34x2

Combine like terms: -27 + 28 = 1
1 + 69x + -68x + -34x2 + -34x2 = -28 + 68x + 34x2 + 28 + -68x + -34x2

Combine like terms: 69x + -68x = 1x
1 + 1x + -34x2 + -34x2 = -28 + 68x + 34x2 + 28 + -68x + -34x2

Combine like terms: -34x2 + -34x2 = -68x2
1 + 1x + -68x2 = -28 + 68x + 34x2 + 28 + -68x + -34x2

Reorder the terms:
1 + 1x + -68x2 = -28 + 28 + 68x + -68x + 34x2 + -34x2

Combine like terms: -28 + 28 = 0
1 + 1x + -68x2 = 0 + 68x + -68x + 34x2 + -34x2
1 + 1x + -68x2 = 68x + -68x + 34x2 + -34x2

Combine like terms: 68x + -68x = 0
1 + 1x + -68x2 = 0 + 34x2 + -34x2
1 + 1x + -68x2 = 34x2 + -34x2

Combine like terms: 34x2 + -34x2 = 0
1 + 1x + -68x2 = 0

Begin completing the square.  Divide all terms by
-68 the coefficient of the squared term: 

Divide each side by '-68'.
-0.01470588235 + -0.01470588235x + x2 = 0

Move the constant term to the right:

Add '0.01470588235' to each side of the equation.
-0.01470588235 + -0.01470588235x + 0.01470588235 + x2 = 0 + 0.01470588235

Reorder the terms:
-0.01470588235 + 0.01470588235 + -0.01470588235x + x2 = 0 + 0.01470588235

Combine like terms: -0.01470588235 + 0.01470588235 = 0.00000000000
0.00000000000 + -0.01470588235x + x2 = 0 + 0.01470588235
-0.01470588235x + x2 = 0 + 0.01470588235

Combine like terms: 0 + 0.01470588235 = 0.01470588235
-0.01470588235x + x2 = 0.01470588235

The x term is -0.01470588235x.  Take half its coefficient (-0.007352941175).
Square it (0.00005406574392) and add it to both sides.

Add '0.00005406574392' to each side of the equation.
-0.01470588235x + 0.00005406574392 + x2 = 0.01470588235 + 0.00005406574392

Reorder the terms:
0.00005406574392 + -0.01470588235x + x2 = 0.01470588235 + 0.00005406574392

Combine like terms: 0.01470588235 + 0.00005406574392 = 0.01475994809392
0.00005406574392 + -0.01470588235x + x2 = 0.01475994809392

Factor a perfect square on the left side:
(x + -0.007352941175)(x + -0.007352941175) = 0.01475994809392

Calculate the square root of the right side: 0.121490527

Break this problem into two subproblems by setting 
(x + -0.007352941175) equal to 0.121490527 and -0.121490527.

Subproblem 1
x + -0.007352941175 = 0.121490527

Simplifying
x + -0.007352941175 = 0.121490527

Reorder the terms:
-0.007352941175 + x = 0.121490527

Solving
-0.007352941175 + x = 0.121490527

Solving for variable 'x'.

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

Add '0.007352941175' to each side of the equation.
-0.007352941175 + 0.007352941175 + x = 0.121490527 + 0.007352941175

Combine like terms: -0.007352941175 + 0.007352941175 = 0.000000000000
0.000000000000 + x = 0.121490527 + 0.007352941175
x = 0.121490527 + 0.007352941175

Combine like terms: 0.121490527 + 0.007352941175 = 0.128843468175
x = 0.128843468175

Simplifying
x = 0.128843468175

Subproblem 2
x + -0.007352941175 = -0.121490527

Simplifying
x + -0.007352941175 = -0.121490527

Reorder the terms:
-0.007352941175 + x = -0.121490527

Solving
-0.007352941175 + x = -0.121490527

Solving for variable 'x'.

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

Add '0.007352941175' to each side of the equation.
-0.007352941175 + 0.007352941175 + x = -0.121490527 + 0.007352941175

Combine like terms: -0.007352941175 + 0.007352941175 = 0.000000000000
0.000000000000 + x = -0.121490527 + 0.007352941175
x = -0.121490527 + 0.007352941175

Combine like terms: -0.121490527 + 0.007352941175 = -0.114137585825
x = -0.114137585825

Simplifying
x = -0.114137585825

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.128843468175, -0.114137585825}