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

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


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

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

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

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

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

Solving
9 + 24x + 16x2 = 225

Solving for variable 'x'.

Reorder the terms:
9 + -225 + 24x + 16x2 = 225 + -225

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

Combine like terms: 225 + -225 = 0
-216 + 24x + 16x2 = 0

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

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

Ignore the factor 8.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-4.5, 3}

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