(5x+3)(5x+3)=(3-2x)(3-2x)

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Solution for (5x+3)(5x+3)=(3-2x)(3-2x) equation: 


Simplifying
(5x + 3)(5x + 3) = (3 + -2x)(3 + -2x)

Reorder the terms:
(3 + 5x)(5x + 3) = (3 + -2x)(3 + -2x)

Reorder the terms:
(3 + 5x)(3 + 5x) = (3 + -2x)(3 + -2x)

Multiply (3 + 5x) * (3 + 5x)
(3(3 + 5x) + 5x * (3 + 5x)) = (3 + -2x)(3 + -2x)
((3 * 3 + 5x * 3) + 5x * (3 + 5x)) = (3 + -2x)(3 + -2x)
((9 + 15x) + 5x * (3 + 5x)) = (3 + -2x)(3 + -2x)
(9 + 15x + (3 * 5x + 5x * 5x)) = (3 + -2x)(3 + -2x)
(9 + 15x + (15x + 25x2)) = (3 + -2x)(3 + -2x)

Combine like terms: 15x + 15x = 30x
(9 + 30x + 25x2) = (3 + -2x)(3 + -2x)

Multiply (3 + -2x) * (3 + -2x)
9 + 30x + 25x2 = (3(3 + -2x) + -2x * (3 + -2x))
9 + 30x + 25x2 = ((3 * 3 + -2x * 3) + -2x * (3 + -2x))
9 + 30x + 25x2 = ((9 + -6x) + -2x * (3 + -2x))
9 + 30x + 25x2 = (9 + -6x + (3 * -2x + -2x * -2x))
9 + 30x + 25x2 = (9 + -6x + (-6x + 4x2))

Combine like terms: -6x + -6x = -12x
9 + 30x + 25x2 = (9 + -12x + 4x2)

Add '-9' to each side of the equation.
9 + 30x + -9 + 25x2 = 9 + -12x + -9 + 4x2

Reorder the terms:
9 + -9 + 30x + 25x2 = 9 + -12x + -9 + 4x2

Combine like terms: 9 + -9 = 0
0 + 30x + 25x2 = 9 + -12x + -9 + 4x2
30x + 25x2 = 9 + -12x + -9 + 4x2

Reorder the terms:
30x + 25x2 = 9 + -9 + -12x + 4x2

Combine like terms: 9 + -9 = 0
30x + 25x2 = 0 + -12x + 4x2
30x + 25x2 = -12x + 4x2

Solving
30x + 25x2 = -12x + 4x2

Solving for variable 'x'.

Reorder the terms:
30x + 12x + 25x2 + -4x2 = -12x + 4x2 + 12x + -4x2

Combine like terms: 30x + 12x = 42x
42x + 25x2 + -4x2 = -12x + 4x2 + 12x + -4x2

Combine like terms: 25x2 + -4x2 = 21x2
42x + 21x2 = -12x + 4x2 + 12x + -4x2

Reorder the terms:
42x + 21x2 = -12x + 12x + 4x2 + -4x2

Combine like terms: -12x + 12x = 0
42x + 21x2 = 0 + 4x2 + -4x2
42x + 21x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
42x + 21x2 = 0

Factor out the Greatest Common Factor (GCF), '21x'.
21x(2 + x) = 0

Ignore the factor 21.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {0, -2}

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