0=(4x+3)(x-5)

Solution for 0=(4x+3)(x-5) equation:

Simplifying
0 = (4x + 3)(x + -5)

Reorder the terms:
0 = (3 + 4x)(x + -5)

Reorder the terms:
0 = (3 + 4x)(-5 + x)

Multiply (3 + 4x) * (-5 + x)
0 = (3(-5 + x) + 4x * (-5 + x))
0 = ((-5 * 3 + x * 3) + 4x * (-5 + x))
0 = ((-15 + 3x) + 4x * (-5 + x))
0 = (-15 + 3x + (-5 * 4x + x * 4x))
0 = (-15 + 3x + (-20x + 4x2))

Combine like terms: 3x + -20x = -17x
0 = (-15 + -17x + 4x2)

Solving
0 = -15 + -17x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + 15 = 15
15 + 17x + -4x2 = -15 + -17x + 4x2 + 15 + 17x + -4x2

Reorder the terms:
15 + 17x + -4x2 = -15 + 15 + -17x + 17x + 4x2 + -4x2

Combine like terms: -15 + 15 = 0
15 + 17x + -4x2 = 0 + -17x + 17x + 4x2 + -4x2
15 + 17x + -4x2 = -17x + 17x + 4x2 + -4x2

Combine like terms: -17x + 17x = 0
15 + 17x + -4x2 = 0 + 4x2 + -4x2
15 + 17x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
15 + 17x + -4x2 = 0

Factor a trinomial.
(5 + -1x)(3 + 4x) = 0

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(3 + 4x)' equal to zero and attempt to solve:

Simplifying
3 + 4x = 0

Solving
3 + 4x = 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 + 4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4x = 0 + -3
4x = 0 + -3

Combine like terms: 0 + -3 = -3
4x = -3

Divide each side by '4'.
x = -0.75

Simplifying
x = -0.75
Solution
x = {5, -0.75}