(2x+4)(2x+7)=

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Solution for (2x+4)(2x+7)= equation: 


Simplifying
(2x + 4)(2x + 7) = 0

Reorder the terms:
(4 + 2x)(2x + 7) = 0

Reorder the terms:
(4 + 2x)(7 + 2x) = 0

Multiply (4 + 2x) * (7 + 2x)
(4(7 + 2x) + 2x * (7 + 2x)) = 0
((7 * 4 + 2x * 4) + 2x * (7 + 2x)) = 0
((28 + 8x) + 2x * (7 + 2x)) = 0
(28 + 8x + (7 * 2x + 2x * 2x)) = 0
(28 + 8x + (14x + 4x2)) = 0

Combine like terms: 8x + 14x = 22x
(28 + 22x + 4x2) = 0

Solving
28 + 22x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + 11x + 2x2) = 0

Factor a trinomial.
2((7 + 2x)(2 + x)) = 0

Ignore the factor 2.

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

Simplifying
7 + 2x = 0

Solving
7 + 2x = 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 + 2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2x = 0 + -7
2x = 0 + -7

Combine like terms: 0 + -7 = -7
2x = -7

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {-3.5, -2}

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