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

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

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

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

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

Multiply (-3 + x) * (3 + 5x)
(-3(3 + 5x) + x(3 + 5x)) = 0
((3 * -3 + 5x * -3) + x(3 + 5x)) = 0
((-9 + -15x) + x(3 + 5x)) = 0
(-9 + -15x + (3 * x + 5x * x)) = 0
(-9 + -15x + (3x + 5x2)) = 0

Combine like terms: -15x + 3x = -12x
(-9 + -12x + 5x2) = 0

Solving
-9 + -12x + 5x2 = 0

Solving for variable 'x'.

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

Subproblem 1
Set the factor '(-3 + -5x)' equal to zero and attempt to solve:

Simplifying
-3 + -5x = 0

Solving
-3 + -5x = 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 + -5x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5x = 0 + 3
-5x = 0 + 3

Combine like terms: 0 + 3 = 3
-5x = 3

Divide each side by '-5'.
x = -0.6

Simplifying
x = -0.6
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 = {-0.6, 3}