(2x+1)(2x+3)=143

Solution for (2x+1)(2x+3)=143 equation:

Simplifying
(2x + 1)(2x + 3) = 143

Reorder the terms:
(1 + 2x)(2x + 3) = 143

Reorder the terms:
(1 + 2x)(3 + 2x) = 143

Multiply (1 + 2x) * (3 + 2x)
(1(3 + 2x) + 2x * (3 + 2x)) = 143
((3 * 1 + 2x * 1) + 2x * (3 + 2x)) = 143
((3 + 2x) + 2x * (3 + 2x)) = 143
(3 + 2x + (3 * 2x + 2x * 2x)) = 143
(3 + 2x + (6x + 4x2)) = 143

Combine like terms: 2x + 6x = 8x
(3 + 8x + 4x2) = 143

Solving
3 + 8x + 4x2 = 143

Solving for variable 'x'.

Reorder the terms:
3 + -143 + 8x + 4x2 = 143 + -143

Combine like terms: 3 + -143 = -140
-140 + 8x + 4x2 = 143 + -143

Combine like terms: 143 + -143 = 0
-140 + 8x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-35 + 2x + x2) = 0

Factor a trinomial.
4((-7 + -1x)(5 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-7, 5}