(-17x+6)(12+4x)=

Solution for (-17x+6)(12+4x)= equation:

Simplifying
(-17x + 6)(12 + 4x) = 0

Reorder the terms:
(6 + -17x)(12 + 4x) = 0

Multiply (6 + -17x) * (12 + 4x)
(6(12 + 4x) + -17x * (12 + 4x)) = 0
((12 * 6 + 4x * 6) + -17x * (12 + 4x)) = 0
((72 + 24x) + -17x * (12 + 4x)) = 0
(72 + 24x + (12 * -17x + 4x * -17x)) = 0
(72 + 24x + (-204x + -68x2)) = 0

Combine like terms: 24x + -204x = -180x
(72 + -180x + -68x2) = 0

Solving
72 + -180x + -68x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(18 + -45x + -17x2) = 0

Factor a trinomial.
4((6 + -17x)(3 + x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(6 + -17x)' equal to zero and attempt to solve:

Simplifying
6 + -17x = 0

Solving
6 + -17x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -17x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -17x = 0 + -6
-17x = 0 + -6

Combine like terms: 0 + -6 = -6
-17x = -6

Divide each side by '-17'.
x = 0.3529411765

Simplifying
x = 0.3529411765
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 = {0.3529411765, -3}