(4x-6)(42x+21)=0

Solution for (4x-6)(42x+21)=0 equation:

Simplifying
(4x + -6)(42x + 21) = 0

Reorder the terms:
(-6 + 4x)(42x + 21) = 0

Reorder the terms:
(-6 + 4x)(21 + 42x) = 0

Multiply (-6 + 4x) * (21 + 42x)
(-6(21 + 42x) + 4x * (21 + 42x)) = 0
((21 * -6 + 42x * -6) + 4x * (21 + 42x)) = 0
((-126 + -252x) + 4x * (21 + 42x)) = 0
(-126 + -252x + (21 * 4x + 42x * 4x)) = 0
(-126 + -252x + (84x + 168x2)) = 0

Combine like terms: -252x + 84x = -168x
(-126 + -168x + 168x2) = 0

Solving
-126 + -168x + 168x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '42'.
42(-3 + -4x + 4x2) = 0

Factor a trinomial.
42((-1 + -2x)(3 + -2x)) = 0

Ignore the factor 42.
Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve:

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

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

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

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
Subproblem 2
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
Solution
x = {-0.5, 1.5}