(2x+3)(2x+3)=49

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Solution for (2x+3)(2x+3)=49 equation: 


Simplifying
(2x + 3)(2x + 3) = 49

Reorder the terms:
(3 + 2x)(2x + 3) = 49

Reorder the terms:
(3 + 2x)(3 + 2x) = 49

Multiply (3 + 2x) * (3 + 2x)
(3(3 + 2x) + 2x * (3 + 2x)) = 49
((3 * 3 + 2x * 3) + 2x * (3 + 2x)) = 49
((9 + 6x) + 2x * (3 + 2x)) = 49
(9 + 6x + (3 * 2x + 2x * 2x)) = 49
(9 + 6x + (6x + 4x2)) = 49

Combine like terms: 6x + 6x = 12x
(9 + 12x + 4x2) = 49

Solving
9 + 12x + 4x2 = 49

Solving for variable 'x'.

Reorder the terms:
9 + -49 + 12x + 4x2 = 49 + -49

Combine like terms: 9 + -49 = -40
-40 + 12x + 4x2 = 49 + -49

Combine like terms: 49 + -49 = 0
-40 + 12x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-10 + 3x + x2) = 0

Factor a trinomial.
4((-5 + -1x)(2 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
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

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 = {-5, 2}

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