3x(x-2)-4x(x-1)=-15

Solution for 3x(x-2)-4x(x-1)=-15 equation:

Simplifying
3x(x + -2) + -4x(x + -1) = -15

Reorder the terms:
3x(-2 + x) + -4x(x + -1) = -15
(-2 * 3x + x * 3x) + -4x(x + -1) = -15
(-6x + 3x2) + -4x(x + -1) = -15

Reorder the terms:
-6x + 3x2 + -4x(-1 + x) = -15
-6x + 3x2 + (-1 * -4x + x * -4x) = -15
-6x + 3x2 + (4x + -4x2) = -15

Reorder the terms:
-6x + 4x + 3x2 + -4x2 = -15

Combine like terms: -6x + 4x = -2x
-2x + 3x2 + -4x2 = -15

Combine like terms: 3x2 + -4x2 = -1x2
-2x + -1x2 = -15

Solving
-2x + -1x2 = -15

Solving for variable 'x'.

Reorder the terms:
15 + -2x + -1x2 = -15 + 15

Combine like terms: -15 + 15 = 0
15 + -2x + -1x2 = 0

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

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

Simplifying
5 + x = 0

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

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

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

Simplifying
x = -5
Solution
x = {3, -5}