(5x+6)(7x-12)=90

Solution for (5x+6)(7x-12)=90 equation:

Simplifying
(5x + 6)(7x + -12) = 90

Reorder the terms:
(6 + 5x)(7x + -12) = 90

Reorder the terms:
(6 + 5x)(-12 + 7x) = 90

Multiply (6 + 5x) * (-12 + 7x)
(6(-12 + 7x) + 5x * (-12 + 7x)) = 90
((-12 * 6 + 7x * 6) + 5x * (-12 + 7x)) = 90
((-72 + 42x) + 5x * (-12 + 7x)) = 90
(-72 + 42x + (-12 * 5x + 7x * 5x)) = 90
(-72 + 42x + (-60x + 35x2)) = 90

Combine like terms: 42x + -60x = -18x
(-72 + -18x + 35x2) = 90

Solving
-72 + -18x + 35x2 = 90

Solving for variable 'x'.

Reorder the terms:
-72 + -90 + -18x + 35x2 = 90 + -90

Combine like terms: -72 + -90 = -162
-162 + -18x + 35x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-162 + -18x + 35x2 = 0

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

Divide each side by '35'.
-4.628571429 + -0.5142857143x + x2 = 0

Move the constant term to the right:

Add '4.628571429' to each side of the equation.
-4.628571429 + -0.5142857143x + 4.628571429 + x2 = 0 + 4.628571429

Reorder the terms:
-4.628571429 + 4.628571429 + -0.5142857143x + x2 = 0 + 4.628571429

Combine like terms: -4.628571429 + 4.628571429 = 0.000000000
0.000000000 + -0.5142857143x + x2 = 0 + 4.628571429
-0.5142857143x + x2 = 0 + 4.628571429

Combine like terms: 0 + 4.628571429 = 4.628571429
-0.5142857143x + x2 = 4.628571429

The x term is -0.5142857143x.  Take half its coefficient (-0.2571428572).
Square it (0.06612244901) and add it to both sides.

Add '0.06612244901' to each side of the equation.
-0.5142857143x + 0.06612244901 + x2 = 4.628571429 + 0.06612244901

Reorder the terms:
0.06612244901 + -0.5142857143x + x2 = 4.628571429 + 0.06612244901

Combine like terms: 4.628571429 + 0.06612244901 = 4.69469387801
0.06612244901 + -0.5142857143x + x2 = 4.69469387801

Factor a perfect square on the left side:
(x + -0.2571428572)(x + -0.2571428572) = 4.69469387801

Calculate the square root of the right side: 2.166724227

Break this problem into two subproblems by setting 
(x + -0.2571428572) equal to 2.166724227 and -2.166724227.

Subproblem 1
x + -0.2571428572 = 2.166724227

Simplifying
x + -0.2571428572 = 2.166724227

Reorder the terms:
-0.2571428572 + x = 2.166724227

Solving
-0.2571428572 + x = 2.166724227

Solving for variable 'x'.

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

Add '0.2571428572' to each side of the equation.
-0.2571428572 + 0.2571428572 + x = 2.166724227 + 0.2571428572

Combine like terms: -0.2571428572 + 0.2571428572 = 0.0000000000
0.0000000000 + x = 2.166724227 + 0.2571428572
x = 2.166724227 + 0.2571428572

Combine like terms: 2.166724227 + 0.2571428572 = 2.4238670842
x = 2.4238670842

Simplifying
x = 2.4238670842

Subproblem 2
x + -0.2571428572 = -2.166724227

Simplifying
x + -0.2571428572 = -2.166724227

Reorder the terms:
-0.2571428572 + x = -2.166724227

Solving
-0.2571428572 + x = -2.166724227

Solving for variable 'x'.

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

Add '0.2571428572' to each side of the equation.
-0.2571428572 + 0.2571428572 + x = -2.166724227 + 0.2571428572

Combine like terms: -0.2571428572 + 0.2571428572 = 0.0000000000
0.0000000000 + x = -2.166724227 + 0.2571428572
x = -2.166724227 + 0.2571428572

Combine like terms: -2.166724227 + 0.2571428572 = -1.9095813698
x = -1.9095813698

Simplifying
x = -1.9095813698

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.4238670842, -1.9095813698}