(2x+1)(2x+3)=35

Solution for (2x+1)(2x+3)=35 equation:

Simplifying
(2x + 1)(2x + 3) = 35

Reorder the terms:
(1 + 2x)(2x + 3) = 35

Reorder the terms:
(1 + 2x)(3 + 2x) = 35

Multiply (1 + 2x) * (3 + 2x)
(1(3 + 2x) + 2x * (3 + 2x)) = 35
((3 * 1 + 2x * 1) + 2x * (3 + 2x)) = 35
((3 + 2x) + 2x * (3 + 2x)) = 35
(3 + 2x + (3 * 2x + 2x * 2x)) = 35
(3 + 2x + (6x + 4x2)) = 35

Combine like terms: 2x + 6x = 8x
(3 + 8x + 4x2) = 35

Solving
3 + 8x + 4x2 = 35

Solving for variable 'x'.

Reorder the terms:
3 + -35 + 8x + 4x2 = 35 + -35

Combine like terms: 3 + -35 = -32
-32 + 8x + 4x2 = 35 + -35

Combine like terms: 35 + -35 = 0
-32 + 8x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-8 + 2x + x2) = 0

Factor a trinomial.
4((-4 + -1x)(2 + -1x)) = 0

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

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-4, 2}