90=(3x+13)(5x-7)

Solution for 90=(3x+13)(5x-7) equation:

Simplifying
90 = (3x + 13)(5x + -7)

Reorder the terms:
90 = (13 + 3x)(5x + -7)

Reorder the terms:
90 = (13 + 3x)(-7 + 5x)

Multiply (13 + 3x) * (-7 + 5x)
90 = (13(-7 + 5x) + 3x * (-7 + 5x))
90 = ((-7 * 13 + 5x * 13) + 3x * (-7 + 5x))
90 = ((-91 + 65x) + 3x * (-7 + 5x))
90 = (-91 + 65x + (-7 * 3x + 5x * 3x))
90 = (-91 + 65x + (-21x + 15x2))

Combine like terms: 65x + -21x = 44x
90 = (-91 + 44x + 15x2)

Solving
90 = -91 + 44x + 15x2

Solving for variable 'x'.

Combine like terms: 90 + 91 = 181
181 + -44x + -15x2 = -91 + 44x + 15x2 + 91 + -44x + -15x2

Reorder the terms:
181 + -44x + -15x2 = -91 + 91 + 44x + -44x + 15x2 + -15x2

Combine like terms: -91 + 91 = 0
181 + -44x + -15x2 = 0 + 44x + -44x + 15x2 + -15x2
181 + -44x + -15x2 = 44x + -44x + 15x2 + -15x2

Combine like terms: 44x + -44x = 0
181 + -44x + -15x2 = 0 + 15x2 + -15x2
181 + -44x + -15x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
181 + -44x + -15x2 = 0

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

Divide each side by '-15'.
-12.06666667 + 2.933333333x + x2 = 0

Move the constant term to the right:

Add '12.06666667' to each side of the equation.
-12.06666667 + 2.933333333x + 12.06666667 + x2 = 0 + 12.06666667

Reorder the terms:
-12.06666667 + 12.06666667 + 2.933333333x + x2 = 0 + 12.06666667

Combine like terms: -12.06666667 + 12.06666667 = 0.00000000
0.00000000 + 2.933333333x + x2 = 0 + 12.06666667
2.933333333x + x2 = 0 + 12.06666667

Combine like terms: 0 + 12.06666667 = 12.06666667
2.933333333x + x2 = 12.06666667

The x term is 2.933333333x.  Take half its coefficient (1.466666667).
Square it (2.151111112) and add it to both sides.

Add '2.151111112' to each side of the equation.
2.933333333x + 2.151111112 + x2 = 12.06666667 + 2.151111112

Reorder the terms:
2.151111112 + 2.933333333x + x2 = 12.06666667 + 2.151111112

Combine like terms: 12.06666667 + 2.151111112 = 14.217777782
2.151111112 + 2.933333333x + x2 = 14.217777782

Factor a perfect square on the left side:
(x + 1.466666667)(x + 1.466666667) = 14.217777782

Calculate the square root of the right side: 3.770646865

Break this problem into two subproblems by setting 
(x + 1.466666667) equal to 3.770646865 and -3.770646865.

Subproblem 1
x + 1.466666667 = 3.770646865

Simplifying
x + 1.466666667 = 3.770646865

Reorder the terms:
1.466666667 + x = 3.770646865

Solving
1.466666667 + x = 3.770646865

Solving for variable 'x'.

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

Add '-1.466666667' to each side of the equation.
1.466666667 + -1.466666667 + x = 3.770646865 + -1.466666667

Combine like terms: 1.466666667 + -1.466666667 = 0.000000000
0.000000000 + x = 3.770646865 + -1.466666667
x = 3.770646865 + -1.466666667

Combine like terms: 3.770646865 + -1.466666667 = 2.303980198
x = 2.303980198

Simplifying
x = 2.303980198

Subproblem 2
x + 1.466666667 = -3.770646865

Simplifying
x + 1.466666667 = -3.770646865

Reorder the terms:
1.466666667 + x = -3.770646865

Solving
1.466666667 + x = -3.770646865

Solving for variable 'x'.

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

Add '-1.466666667' to each side of the equation.
1.466666667 + -1.466666667 + x = -3.770646865 + -1.466666667

Combine like terms: 1.466666667 + -1.466666667 = 0.000000000
0.000000000 + x = -3.770646865 + -1.466666667
x = -3.770646865 + -1.466666667

Combine like terms: -3.770646865 + -1.466666667 = -5.237313532
x = -5.237313532

Simplifying
x = -5.237313532

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.303980198, -5.237313532}