4(x+17)(x-3)=0

Solution for 4(x+17)(x-3)=0 equation:

Simplifying
4(x + 17)(x + -3) = 0

Reorder the terms:
4(17 + x)(x + -3) = 0

Reorder the terms:
4(17 + x)(-3 + x) = 0

Multiply (17 + x) * (-3 + x)
4(17(-3 + x) + x(-3 + x)) = 0
4((-3 * 17 + x * 17) + x(-3 + x)) = 0
4((-51 + 17x) + x(-3 + x)) = 0
4(-51 + 17x + (-3 * x + x * x)) = 0
4(-51 + 17x + (-3x + x2)) = 0

Combine like terms: 17x + -3x = 14x
4(-51 + 14x + x2) = 0
(-51 * 4 + 14x * 4 + x2 * 4) = 0
(-204 + 56x + 4x2) = 0

Solving
-204 + 56x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-51 + 14x + x2) = 0

Factor a trinomial.
4((-17 + -1x)(3 + -1x)) = 0

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

Simplifying
-17 + -1x = 0

Solving
-17 + -1x = 0

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

Add '17' to each side of the equation.
-17 + 17 + -1x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1x = 0 + 17
-1x = 0 + 17

Combine like terms: 0 + 17 = 17
-1x = 17

Divide each side by '-1'.
x = -17

Simplifying
x = -17
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-17, 3}