(x+3)(-4x+6)=0

Solution for (x+3)(-4x+6)=0 equation:

Simplifying
(x + 3)(-4x + 6) = 0

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

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

Multiply (3 + x) * (6 + -4x)
(3(6 + -4x) + x(6 + -4x)) = 0
((6 * 3 + -4x * 3) + x(6 + -4x)) = 0
((18 + -12x) + x(6 + -4x)) = 0
(18 + -12x + (6 * x + -4x * x)) = 0
(18 + -12x + (6x + -4x2)) = 0

Combine like terms: -12x + 6x = -6x
(18 + -6x + -4x2) = 0

Solving
18 + -6x + -4x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 2.
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 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

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

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

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

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