multiply the binomials: (4x+3)(2x-5)

Use the extended distributive property FOIL (First, Outside, Inside, Last):

(4x+ 3)(2x - 5)  =  (4x)(2x) + (4x)(-5) + (3)(2x) + (3)(-5)  =  8x² - 20x + 6x - 15  =  8x² - 14x - 15

Simplifying
 4x + 3 = 2x + -5
 
 Reorder the terms:
 3 + 4x = 2x + -5
 
 Reorder the terms:
 3 + 4x = -5 + 2x
 
 Solving
 3 + 4x = -5 + 2x
 
 Solving for variable 'x'.
 
 Move all terms containing x to the left, all other terms to the right.
 
 Add '-2x' to each side of the equation.
 3 + 4x + -2x = -5 + 2x + -2x
 
 Combine like terms: 4x + -2x = 2x
 3 + 2x = -5 + 2x + -2x
 
 Combine like terms: 2x + -2x = 0
 3 + 2x = -5 + 0
 3 + 2x = -5
 
 Add '-3' to each side of the equation.
 3 + -3 + 2x = -5 + -3
 
 Combine like terms: 3 + -3 = 0
 0 + 2x = -5 + -3
 2x = -5 + -3
 
 Combine like terms: -5 + -3 = -8
 2x = -8
 
 Divide each side by '2'.
 x = -4
 
 Simplifying
 x = -4