3(3x-1)+5(5x+1)=3*(3x-1)*(5x+1)

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Solution for 3(3x-1)+5(5x+1)=3*(3x-1)*(5x+1) equation: 


Simplifying
3(3x + -1) + 5(5x + 1) = 3(3x + -1)(5x + 1)

Reorder the terms:
3(-1 + 3x) + 5(5x + 1) = 3(3x + -1)(5x + 1)
(-1 * 3 + 3x * 3) + 5(5x + 1) = 3(3x + -1)(5x + 1)
(-3 + 9x) + 5(5x + 1) = 3(3x + -1)(5x + 1)

Reorder the terms:
-3 + 9x + 5(1 + 5x) = 3(3x + -1)(5x + 1)
-3 + 9x + (1 * 5 + 5x * 5) = 3(3x + -1)(5x + 1)
-3 + 9x + (5 + 25x) = 3(3x + -1)(5x + 1)

Reorder the terms:
-3 + 5 + 9x + 25x = 3(3x + -1)(5x + 1)

Combine like terms: -3 + 5 = 2
2 + 9x + 25x = 3(3x + -1)(5x + 1)

Combine like terms: 9x + 25x = 34x
2 + 34x = 3(3x + -1)(5x + 1)

Reorder the terms:
2 + 34x = 3(-1 + 3x)(5x + 1)

Reorder the terms:
2 + 34x = 3(-1 + 3x)(1 + 5x)

Multiply (-1 + 3x) * (1 + 5x)
2 + 34x = 3(-1(1 + 5x) + 3x * (1 + 5x))
2 + 34x = 3((1 * -1 + 5x * -1) + 3x * (1 + 5x))
2 + 34x = 3((-1 + -5x) + 3x * (1 + 5x))
2 + 34x = 3(-1 + -5x + (1 * 3x + 5x * 3x))
2 + 34x = 3(-1 + -5x + (3x + 15x2))

Combine like terms: -5x + 3x = -2x
2 + 34x = 3(-1 + -2x + 15x2)
2 + 34x = (-1 * 3 + -2x * 3 + 15x2 * 3)
2 + 34x = (-3 + -6x + 45x2)

Solving
2 + 34x = -3 + -6x + 45x2

Solving for variable 'x'.

Reorder the terms:
2 + 3 + 34x + 6x + -45x2 = -3 + -6x + 45x2 + 3 + 6x + -45x2

Combine like terms: 2 + 3 = 5
5 + 34x + 6x + -45x2 = -3 + -6x + 45x2 + 3 + 6x + -45x2

Combine like terms: 34x + 6x = 40x
5 + 40x + -45x2 = -3 + -6x + 45x2 + 3 + 6x + -45x2

Reorder the terms:
5 + 40x + -45x2 = -3 + 3 + -6x + 6x + 45x2 + -45x2

Combine like terms: -3 + 3 = 0
5 + 40x + -45x2 = 0 + -6x + 6x + 45x2 + -45x2
5 + 40x + -45x2 = -6x + 6x + 45x2 + -45x2

Combine like terms: -6x + 6x = 0
5 + 40x + -45x2 = 0 + 45x2 + -45x2
5 + 40x + -45x2 = 45x2 + -45x2

Combine like terms: 45x2 + -45x2 = 0
5 + 40x + -45x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(1 + 8x + -9x2) = 0

Factor a trinomial.
5((1 + -1x)(1 + 9x)) = 0

Ignore the factor 5.

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 '(1 + 9x)' equal to zero and attempt to solve:

Simplifying
1 + 9x = 0

Solving
1 + 9x = 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 + 9x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 9x = 0 + -1
9x = 0 + -1

Combine like terms: 0 + -1 = -1
9x = -1

Divide each side by '9'.
x = -0.1111111111

Simplifying
x = -0.1111111111
Solution
x = {1, -0.1111111111}

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