7x+74=(3x+6)(3x+6)

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Solution for 7x+74=(3x+6)(3x+6) equation: 


Simplifying
7x + 74 = (3x + 6)(3x + 6)

Reorder the terms:
74 + 7x = (3x + 6)(3x + 6)

Reorder the terms:
74 + 7x = (6 + 3x)(3x + 6)

Reorder the terms:
74 + 7x = (6 + 3x)(6 + 3x)

Multiply (6 + 3x) * (6 + 3x)
74 + 7x = (6(6 + 3x) + 3x * (6 + 3x))
74 + 7x = ((6 * 6 + 3x * 6) + 3x * (6 + 3x))
74 + 7x = ((36 + 18x) + 3x * (6 + 3x))
74 + 7x = (36 + 18x + (6 * 3x + 3x * 3x))
74 + 7x = (36 + 18x + (18x + 9x2))

Combine like terms: 18x + 18x = 36x
74 + 7x = (36 + 36x + 9x2)

Solving
74 + 7x = 36 + 36x + 9x2

Solving for variable 'x'.

Reorder the terms:
74 + -36 + 7x + -36x + -9x2 = 36 + 36x + 9x2 + -36 + -36x + -9x2

Combine like terms: 74 + -36 = 38
38 + 7x + -36x + -9x2 = 36 + 36x + 9x2 + -36 + -36x + -9x2

Combine like terms: 7x + -36x = -29x
38 + -29x + -9x2 = 36 + 36x + 9x2 + -36 + -36x + -9x2

Reorder the terms:
38 + -29x + -9x2 = 36 + -36 + 36x + -36x + 9x2 + -9x2

Combine like terms: 36 + -36 = 0
38 + -29x + -9x2 = 0 + 36x + -36x + 9x2 + -9x2
38 + -29x + -9x2 = 36x + -36x + 9x2 + -9x2

Combine like terms: 36x + -36x = 0
38 + -29x + -9x2 = 0 + 9x2 + -9x2
38 + -29x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
38 + -29x + -9x2 = 0

Factor a trinomial.
(1 + -1x)(38 + 9x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(38 + 9x)' equal to zero and attempt to solve:

Simplifying
38 + 9x = 0

Solving
38 + 9x = 0

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

Add '-38' to each side of the equation.
38 + -38 + 9x = 0 + -38

Combine like terms: 38 + -38 = 0
0 + 9x = 0 + -38
9x = 0 + -38

Combine like terms: 0 + -38 = -38
9x = -38

Divide each side by '9'.
x = -4.222222222

Simplifying
x = -4.222222222
Solution
x = {1, -4.222222222}

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