(x+3)(2x-4)=70

Solution for (x+3)(2x-4)=70 equation:

Simplifying
(x + 3)(2x + -4) = 70

Reorder the terms:
(3 + x)(2x + -4) = 70

Reorder the terms:
(3 + x)(-4 + 2x) = 70

Multiply (3 + x) * (-4 + 2x)
(3(-4 + 2x) + x(-4 + 2x)) = 70
((-4 * 3 + 2x * 3) + x(-4 + 2x)) = 70
((-12 + 6x) + x(-4 + 2x)) = 70
(-12 + 6x + (-4 * x + 2x * x)) = 70
(-12 + 6x + (-4x + 2x2)) = 70

Combine like terms: 6x + -4x = 2x
(-12 + 2x + 2x2) = 70

Solving
-12 + 2x + 2x2 = 70

Solving for variable 'x'.

Reorder the terms:
-12 + -70 + 2x + 2x2 = 70 + -70

Combine like terms: -12 + -70 = -82
-82 + 2x + 2x2 = 70 + -70

Combine like terms: 70 + -70 = 0
-82 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-41 + x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-41 + x + x2)' equal to zero and attempt to solve:

Simplifying
-41 + x + x2 = 0

Solving
-41 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '41' to each side of the equation.
-41 + x + 41 + x2 = 0 + 41

Reorder the terms:
-41 + 41 + x + x2 = 0 + 41

Combine like terms: -41 + 41 = 0
0 + x + x2 = 0 + 41
x + x2 = 0 + 41

Combine like terms: 0 + 41 = 41
x + x2 = 41

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 41 + 0.25

Reorder the terms:
0.25 + x + x2 = 41 + 0.25

Combine like terms: 41 + 0.25 = 41.25
0.25 + x + x2 = 41.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 41.25

Calculate the square root of the right side: 6.422616289

Break this problem into two subproblems by setting 
(x + 0.5) equal to 6.422616289 and -6.422616289.

Subproblem 1
x + 0.5 = 6.422616289

Simplifying
x + 0.5 = 6.422616289

Reorder the terms:
0.5 + x = 6.422616289

Solving
0.5 + x = 6.422616289

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 6.422616289 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 6.422616289 + -0.5
x = 6.422616289 + -0.5

Combine like terms: 6.422616289 + -0.5 = 5.922616289
x = 5.922616289

Simplifying
x = 5.922616289

Subproblem 2
x + 0.5 = -6.422616289

Simplifying
x + 0.5 = -6.422616289

Reorder the terms:
0.5 + x = -6.422616289

Solving
0.5 + x = -6.422616289

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -6.422616289 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -6.422616289 + -0.5
x = -6.422616289 + -0.5

Combine like terms: -6.422616289 + -0.5 = -6.922616289
x = -6.922616289

Simplifying
x = -6.922616289

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.922616289, -6.922616289}
Solution
x = {5.922616289, -6.922616289}