(2x+4)(2x+5)=306

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Solution for (2x+4)(2x+5)=306 equation: 


Simplifying
(2x + 4)(2x + 5) = 306

Reorder the terms:
(4 + 2x)(2x + 5) = 306

Reorder the terms:
(4 + 2x)(5 + 2x) = 306

Multiply (4 + 2x) * (5 + 2x)
(4(5 + 2x) + 2x * (5 + 2x)) = 306
((5 * 4 + 2x * 4) + 2x * (5 + 2x)) = 306
((20 + 8x) + 2x * (5 + 2x)) = 306
(20 + 8x + (5 * 2x + 2x * 2x)) = 306
(20 + 8x + (10x + 4x2)) = 306

Combine like terms: 8x + 10x = 18x
(20 + 18x + 4x2) = 306

Solving
20 + 18x + 4x2 = 306

Solving for variable 'x'.

Reorder the terms:
20 + -306 + 18x + 4x2 = 306 + -306

Combine like terms: 20 + -306 = -286
-286 + 18x + 4x2 = 306 + -306

Combine like terms: 306 + -306 = 0
-286 + 18x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-143 + 9x + 2x2) = 0

Factor a trinomial.
2((-11 + -1x)(13 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11

Subproblem 2
Set the factor '(13 + -2x)' equal to zero and attempt to solve:

Simplifying
13 + -2x = 0

Solving
13 + -2x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -2x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2x = 0 + -13
-2x = 0 + -13

Combine like terms: 0 + -13 = -13
-2x = -13

Divide each side by '-2'.
x = 6.5

Simplifying
x = 6.5
Solution
x = {-11, 6.5}

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