(4+2x)(7+2x)=54

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Solution for (4+2x)(7+2x)=54 equation: 


Simplifying
(4 + 2x)(7 + 2x) = 54

Multiply (4 + 2x) * (7 + 2x)
(4(7 + 2x) + 2x * (7 + 2x)) = 54
((7 * 4 + 2x * 4) + 2x * (7 + 2x)) = 54
((28 + 8x) + 2x * (7 + 2x)) = 54
(28 + 8x + (7 * 2x + 2x * 2x)) = 54
(28 + 8x + (14x + 4x2)) = 54

Combine like terms: 8x + 14x = 22x
(28 + 22x + 4x2) = 54

Solving
28 + 22x + 4x2 = 54

Solving for variable 'x'.

Reorder the terms:
28 + -54 + 22x + 4x2 = 54 + -54

Combine like terms: 28 + -54 = -26
-26 + 22x + 4x2 = 54 + -54

Combine like terms: 54 + -54 = 0
-26 + 22x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + 11x + 2x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-6.5, 1}

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