(2x-3)(4x+6)=0

Solution for (2x-3)(4x+6)=0 equation:

Simplifying
(2x + -3)(4x + 6) = 0

Reorder the terms:
(-3 + 2x)(4x + 6) = 0

Reorder the terms:
(-3 + 2x)(6 + 4x) = 0

Multiply (-3 + 2x) * (6 + 4x)
(-3(6 + 4x) + 2x * (6 + 4x)) = 0
((6 * -3 + 4x * -3) + 2x * (6 + 4x)) = 0
((-18 + -12x) + 2x * (6 + 4x)) = 0
(-18 + -12x + (6 * 2x + 4x * 2x)) = 0
(-18 + -12x + (12x + 8x2)) = 0

Combine like terms: -12x + 12x = 0
(-18 + 0 + 8x2) = 0
(-18 + 8x2) = 0

Solving
-18 + 8x2 = 0

Solving for variable 'x'.

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

Add '18' to each side of the equation.
-18 + 18 + 8x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 8x2 = 0 + 18
8x2 = 0 + 18

Combine like terms: 0 + 18 = 18
8x2 = 18

Divide each side by '8'.
x2 = 2.25

Simplifying
x2 = 2.25

Take the square root of each side:
x = {-1.5, 1.5}