(51x+3)(1+52x)=

Solution for (51x+3)(1+52x)= equation:

Simplifying
(51x + 3)(1 + 52x) = 0

Reorder the terms:
(3 + 51x)(1 + 52x) = 0

Multiply (3 + 51x) * (1 + 52x)
(3(1 + 52x) + 51x * (1 + 52x)) = 0
((1 * 3 + 52x * 3) + 51x * (1 + 52x)) = 0
((3 + 156x) + 51x * (1 + 52x)) = 0
(3 + 156x + (1 * 51x + 52x * 51x)) = 0
(3 + 156x + (51x + 2652x2)) = 0

Combine like terms: 156x + 51x = 207x
(3 + 207x + 2652x2) = 0

Solving
3 + 207x + 2652x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 69x + 884x2) = 0

Factor a trinomial.
3((1 + 17x)(1 + 52x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + 17x)' equal to zero and attempt to solve:

Simplifying
1 + 17x = 0

Solving
1 + 17x = 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 + 17x = 0 + -1

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

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

Divide each side by '17'.
x = -0.05882352941

Simplifying
x = -0.05882352941
Subproblem 2
Set the factor '(1 + 52x)' equal to zero and attempt to solve:

Simplifying
1 + 52x = 0

Solving
1 + 52x = 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 + 52x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 52x = 0 + -1
52x = 0 + -1

Combine like terms: 0 + -1 = -1
52x = -1

Divide each side by '52'.
x = -0.01923076923

Simplifying
x = -0.01923076923
Solution
x = {-0.05882352941, -0.01923076923}