(x-3)(10x+15)=0

Solution for (x-3)(10x+15)=0 equation:

Simplifying
(x + -3)(10x + 15) = 0

Reorder the terms:
(-3 + x)(10x + 15) = 0

Reorder the terms:
(-3 + x)(15 + 10x) = 0

Multiply (-3 + x) * (15 + 10x)
(-3(15 + 10x) + x(15 + 10x)) = 0
((15 * -3 + 10x * -3) + x(15 + 10x)) = 0
((-45 + -30x) + x(15 + 10x)) = 0
(-45 + -30x + (15 * x + 10x * x)) = 0
(-45 + -30x + (15x + 10x2)) = 0

Combine like terms: -30x + 15x = -15x
(-45 + -15x + 10x2) = 0

Solving
-45 + -15x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-9 + -3x + 2x2) = 0

Factor a trinomial.
5((-3 + -2x)(3 + -1x)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5
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 = {-1.5, 3}