-5(4x-6)(x-1)=0

Solution for -5(4x-6)(x-1)=0 equation:

Simplifying
-5(4x + -6)(x + -1) = 0

Reorder the terms:
-5(-6 + 4x)(x + -1) = 0

Reorder the terms:
-5(-6 + 4x)(-1 + x) = 0

Multiply (-6 + 4x) * (-1 + x)
-5(-6(-1 + x) + 4x * (-1 + x)) = 0
-5((-1 * -6 + x * -6) + 4x * (-1 + x)) = 0
-5((6 + -6x) + 4x * (-1 + x)) = 0
-5(6 + -6x + (-1 * 4x + x * 4x)) = 0
-5(6 + -6x + (-4x + 4x2)) = 0

Combine like terms: -6x + -4x = -10x
-5(6 + -10x + 4x2) = 0
(6 * -5 + -10x * -5 + 4x2 * -5) = 0
(-30 + 50x + -20x2) = 0

Solving
-30 + 50x + -20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-3 + 5x + -2x2) = 0

Factor a trinomial.
10((-3 + 2x)(1 + -1x)) = 0

Ignore the factor 10.
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 '(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
Solution
x = {1.5, 1}