(5x-7)(6x+4)=12

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Solution for (5x-7)(6x+4)=12 equation: 


Simplifying
(5x + -7)(6x + 4) = 12

Reorder the terms:
(-7 + 5x)(6x + 4) = 12

Reorder the terms:
(-7 + 5x)(4 + 6x) = 12

Multiply (-7 + 5x) * (4 + 6x)
(-7(4 + 6x) + 5x * (4 + 6x)) = 12
((4 * -7 + 6x * -7) + 5x * (4 + 6x)) = 12
((-28 + -42x) + 5x * (4 + 6x)) = 12
(-28 + -42x + (4 * 5x + 6x * 5x)) = 12
(-28 + -42x + (20x + 30x2)) = 12

Combine like terms: -42x + 20x = -22x
(-28 + -22x + 30x2) = 12

Solving
-28 + -22x + 30x2 = 12

Solving for variable 'x'.

Reorder the terms:
-28 + -12 + -22x + 30x2 = 12 + -12

Combine like terms: -28 + -12 = -40
-40 + -22x + 30x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-40 + -22x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + -11x + 15x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-20 + -11x + 15x2)' equal to zero and attempt to solve:

Simplifying
-20 + -11x + 15x2 = 0

Solving
-20 + -11x + 15x2 = 0

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

Divide each side by '15'.
-1.333333333 + -0.7333333333x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -0.7333333333x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -0.7333333333x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -0.7333333333x + x2 = 0 + 1.333333333
-0.7333333333x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-0.7333333333x + x2 = 1.333333333

The x term is -0.7333333333x.  Take half its coefficient (-0.3666666667).
Square it (0.1344444445) and add it to both sides.

Add '0.1344444445' to each side of the equation.
-0.7333333333x + 0.1344444445 + x2 = 1.333333333 + 0.1344444445

Reorder the terms:
0.1344444445 + -0.7333333333x + x2 = 1.333333333 + 0.1344444445

Combine like terms: 1.333333333 + 0.1344444445 = 1.4677777775
0.1344444445 + -0.7333333333x + x2 = 1.4677777775

Factor a perfect square on the left side:
(x + -0.3666666667)(x + -0.3666666667) = 1.4677777775

Calculate the square root of the right side: 1.21151879

Break this problem into two subproblems by setting 
(x + -0.3666666667) equal to 1.21151879 and -1.21151879.


Subproblem 1
x + -0.3666666667 = 1.21151879

Simplifying
x + -0.3666666667 = 1.21151879

Reorder the terms:
-0.3666666667 + x = 1.21151879

Solving
-0.3666666667 + x = 1.21151879

Solving for variable 'x'.

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

Add '0.3666666667' to each side of the equation.
-0.3666666667 + 0.3666666667 + x = 1.21151879 + 0.3666666667

Combine like terms: -0.3666666667 + 0.3666666667 = 0.0000000000
0.0000000000 + x = 1.21151879 + 0.3666666667
x = 1.21151879 + 0.3666666667

Combine like terms: 1.21151879 + 0.3666666667 = 1.5781854567
x = 1.5781854567

Simplifying
x = 1.5781854567


Subproblem 2
x + -0.3666666667 = -1.21151879

Simplifying
x + -0.3666666667 = -1.21151879

Reorder the terms:
-0.3666666667 + x = -1.21151879

Solving
-0.3666666667 + x = -1.21151879

Solving for variable 'x'.

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

Add '0.3666666667' to each side of the equation.
-0.3666666667 + 0.3666666667 + x = -1.21151879 + 0.3666666667

Combine like terms: -0.3666666667 + 0.3666666667 = 0.0000000000
0.0000000000 + x = -1.21151879 + 0.3666666667
x = -1.21151879 + 0.3666666667

Combine like terms: -1.21151879 + 0.3666666667 = -0.8448521233
x = -0.8448521233

Simplifying
x = -0.8448521233


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5781854567, -0.8448521233}
Solution
x = {1.5781854567, -0.8448521233}

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