7x+18=(2x+3)(2x+3)

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Solution for 7x+18=(2x+3)(2x+3) equation: 


Simplifying
7x + 18 = (2x + 3)(2x + 3)

Reorder the terms:
18 + 7x = (2x + 3)(2x + 3)

Reorder the terms:
18 + 7x = (3 + 2x)(2x + 3)

Reorder the terms:
18 + 7x = (3 + 2x)(3 + 2x)

Multiply (3 + 2x) * (3 + 2x)
18 + 7x = (3(3 + 2x) + 2x * (3 + 2x))
18 + 7x = ((3 * 3 + 2x * 3) + 2x * (3 + 2x))
18 + 7x = ((9 + 6x) + 2x * (3 + 2x))
18 + 7x = (9 + 6x + (3 * 2x + 2x * 2x))
18 + 7x = (9 + 6x + (6x + 4x2))

Combine like terms: 6x + 6x = 12x
18 + 7x = (9 + 12x + 4x2)

Solving
18 + 7x = 9 + 12x + 4x2

Solving for variable 'x'.

Reorder the terms:
18 + -9 + 7x + -12x + -4x2 = 9 + 12x + 4x2 + -9 + -12x + -4x2

Combine like terms: 18 + -9 = 9
9 + 7x + -12x + -4x2 = 9 + 12x + 4x2 + -9 + -12x + -4x2

Combine like terms: 7x + -12x = -5x
9 + -5x + -4x2 = 9 + 12x + 4x2 + -9 + -12x + -4x2

Reorder the terms:
9 + -5x + -4x2 = 9 + -9 + 12x + -12x + 4x2 + -4x2

Combine like terms: 9 + -9 = 0
9 + -5x + -4x2 = 0 + 12x + -12x + 4x2 + -4x2
9 + -5x + -4x2 = 12x + -12x + 4x2 + -4x2

Combine like terms: 12x + -12x = 0
9 + -5x + -4x2 = 0 + 4x2 + -4x2
9 + -5x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
9 + -5x + -4x2 = 0

Factor a trinomial.
(1 + -1x)(9 + 4x) = 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 '(9 + 4x)' equal to zero and attempt to solve:

Simplifying
9 + 4x = 0

Solving
9 + 4x = 0

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

Add '-9' to each side of the equation.
9 + -9 + 4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 4x = 0 + -9
4x = 0 + -9

Combine like terms: 0 + -9 = -9
4x = -9

Divide each side by '4'.
x = -2.25

Simplifying
x = -2.25
Solution
x = {1, -2.25}

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