(5x+3)(4x-7)=90

Solution for (5x+3)(4x-7)=90 equation:

Simplifying
(5x + 3)(4x + -7) = 90

Reorder the terms:
(3 + 5x)(4x + -7) = 90

Reorder the terms:
(3 + 5x)(-7 + 4x) = 90

Multiply (3 + 5x) * (-7 + 4x)
(3(-7 + 4x) + 5x * (-7 + 4x)) = 90
((-7 * 3 + 4x * 3) + 5x * (-7 + 4x)) = 90
((-21 + 12x) + 5x * (-7 + 4x)) = 90
(-21 + 12x + (-7 * 5x + 4x * 5x)) = 90
(-21 + 12x + (-35x + 20x2)) = 90

Combine like terms: 12x + -35x = -23x
(-21 + -23x + 20x2) = 90

Solving
-21 + -23x + 20x2 = 90

Solving for variable 'x'.

Reorder the terms:
-21 + -90 + -23x + 20x2 = 90 + -90

Combine like terms: -21 + -90 = -111
-111 + -23x + 20x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-111 + -23x + 20x2 = 0

Factor a trinomial.
(-37 + -20x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-37 + -20x)' equal to zero and attempt to solve:

Simplifying
-37 + -20x = 0

Solving
-37 + -20x = 0

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

Add '37' to each side of the equation.
-37 + 37 + -20x = 0 + 37

Combine like terms: -37 + 37 = 0
0 + -20x = 0 + 37
-20x = 0 + 37

Combine like terms: 0 + 37 = 37
-20x = 37

Divide each side by '-20'.
x = -1.85

Simplifying
x = -1.85
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1.85, 3}