(2x+1)(2x+3)=99

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Solution for (2x+1)(2x+3)=99 equation:


Simplifying
(2x + 1)(2x + 3) = 99

Reorder the terms:
(1 + 2x)(2x + 3) = 99

Reorder the terms:
(1 + 2x)(3 + 2x) = 99

Multiply (1 + 2x) * (3 + 2x)
(1(3 + 2x) + 2x * (3 + 2x)) = 99
((3 * 1 + 2x * 1) + 2x * (3 + 2x)) = 99
((3 + 2x) + 2x * (3 + 2x)) = 99
(3 + 2x + (3 * 2x + 2x * 2x)) = 99
(3 + 2x + (6x + 4x2)) = 99

Combine like terms: 2x + 6x = 8x
(3 + 8x + 4x2) = 99

Solving
3 + 8x + 4x2 = 99

Solving for variable 'x'.

Reorder the terms:
3 + -99 + 8x + 4x2 = 99 + -99

Combine like terms: 3 + -99 = -96
-96 + 8x + 4x2 = 99 + -99

Combine like terms: 99 + -99 = 0
-96 + 8x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-24 + 2x + x2) = 0

Factor a trinomial.
4((-6 + -1x)(4 + -1x)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 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 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6

Subproblem 2

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

Solution

x = {-6, 4}

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