-3(x-1)(5-2x)=0

Solution for -3(x-1)(5-2x)=0 equation:

Simplifying
-3(x + -1)(5 + -2x) = 0

Reorder the terms:
-3(-1 + x)(5 + -2x) = 0

Multiply (-1 + x) * (5 + -2x)
-3(-1(5 + -2x) + x(5 + -2x)) = 0
-3((5 * -1 + -2x * -1) + x(5 + -2x)) = 0
-3((-5 + 2x) + x(5 + -2x)) = 0
-3(-5 + 2x + (5 * x + -2x * x)) = 0
-3(-5 + 2x + (5x + -2x2)) = 0

Combine like terms: 2x + 5x = 7x
-3(-5 + 7x + -2x2) = 0
(-5 * -3 + 7x * -3 + -2x2 * -3) = 0
(15 + -21x + 6x2) = 0

Solving
15 + -21x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + -7x + 2x2) = 0

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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

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

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {1, 2.5}