(7x-3)(4x+6)=0

Solution for (7x-3)(4x+6)=0 equation:

Simplifying
(7x + -3)(4x + 6) = 0

Reorder the terms:
(-3 + 7x)(4x + 6) = 0

Reorder the terms:
(-3 + 7x)(6 + 4x) = 0

Multiply (-3 + 7x) * (6 + 4x)
(-3(6 + 4x) + 7x * (6 + 4x)) = 0
((6 * -3 + 4x * -3) + 7x * (6 + 4x)) = 0
((-18 + -12x) + 7x * (6 + 4x)) = 0
(-18 + -12x + (6 * 7x + 4x * 7x)) = 0
(-18 + -12x + (42x + 28x2)) = 0

Combine like terms: -12x + 42x = 30x
(-18 + 30x + 28x2) = 0

Solving
-18 + 30x + 28x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 15x + 14x2) = 0

Factor a trinomial.
2((-3 + -2x)(3 + -7x)) = 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 + -7x)' equal to zero and attempt to solve:

Simplifying
3 + -7x = 0

Solving
3 + -7x = 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 + -7x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7x = 0 + -3
-7x = 0 + -3

Combine like terms: 0 + -3 = -3
-7x = -3

Divide each side by '-7'.
x = 0.4285714286

Simplifying
x = 0.4285714286
Solution
x = {-1.5, 0.4285714286}