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

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


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

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

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

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

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

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

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

Solving
9 + 30x + 25x2 = 4 + -12x + 9x2

Solving for variable 'x'.

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

Combine like terms: 9 + -4 = 5
5 + 30x + 12x + 25x2 + -9x2 = 4 + -12x + 9x2 + -4 + 12x + -9x2

Combine like terms: 30x + 12x = 42x
5 + 42x + 25x2 + -9x2 = 4 + -12x + 9x2 + -4 + 12x + -9x2

Combine like terms: 25x2 + -9x2 = 16x2
5 + 42x + 16x2 = 4 + -12x + 9x2 + -4 + 12x + -9x2

Reorder the terms:
5 + 42x + 16x2 = 4 + -4 + -12x + 12x + 9x2 + -9x2

Combine like terms: 4 + -4 = 0
5 + 42x + 16x2 = 0 + -12x + 12x + 9x2 + -9x2
5 + 42x + 16x2 = -12x + 12x + 9x2 + -9x2

Combine like terms: -12x + 12x = 0
5 + 42x + 16x2 = 0 + 9x2 + -9x2
5 + 42x + 16x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
5 + 42x + 16x2 = 0

Factor a trinomial.
(5 + 2x)(1 + 8x) = 0


Subproblem 1
Set the factor '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 2
Set the factor '(1 + 8x)' equal to zero and attempt to solve:

Simplifying
1 + 8x = 0

Solving
1 + 8x = 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 + 8x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 8x = 0 + -1
8x = 0 + -1

Combine like terms: 0 + -1 = -1
8x = -1

Divide each side by '8'.
x = -0.125

Simplifying
x = -0.125
Solution
x = {-2.5, -0.125}

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