225=(4x+3)(4x+3)

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Solution for 225=(4x+3)(4x+3) equation: 


Simplifying
225 = (4x + 3)(4x + 3)

Reorder the terms:
225 = (3 + 4x)(4x + 3)

Reorder the terms:
225 = (3 + 4x)(3 + 4x)

Multiply (3 + 4x) * (3 + 4x)
225 = (3(3 + 4x) + 4x * (3 + 4x))
225 = ((3 * 3 + 4x * 3) + 4x * (3 + 4x))
225 = ((9 + 12x) + 4x * (3 + 4x))
225 = (9 + 12x + (3 * 4x + 4x * 4x))
225 = (9 + 12x + (12x + 16x2))

Combine like terms: 12x + 12x = 24x
225 = (9 + 24x + 16x2)

Solving
225 = 9 + 24x + 16x2

Solving for variable 'x'.

Combine like terms: 225 + -9 = 216
216 + -24x + -16x2 = 9 + 24x + 16x2 + -9 + -24x + -16x2

Reorder the terms:
216 + -24x + -16x2 = 9 + -9 + 24x + -24x + 16x2 + -16x2

Combine like terms: 9 + -9 = 0
216 + -24x + -16x2 = 0 + 24x + -24x + 16x2 + -16x2
216 + -24x + -16x2 = 24x + -24x + 16x2 + -16x2

Combine like terms: 24x + -24x = 0
216 + -24x + -16x2 = 0 + 16x2 + -16x2
216 + -24x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
216 + -24x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(27 + -3x + -2x2) = 0

Factor a trinomial.
8((3 + -1x)(9 + 2x)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

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

Simplifying
9 + 2x = 0

Solving
9 + 2x = 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 + 2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2x = 0 + -9
2x = 0 + -9

Combine like terms: 0 + -9 = -9
2x = -9

Divide each side by '2'.
x = -4.5

Simplifying
x = -4.5
Solution
x = {3, -4.5}

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