0=(5x+3)(x-3)

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Solution for 0=(5x+3)(x-3) equation: 


Simplifying
0 = (5x + 3)(x + -3)

Reorder the terms:
0 = (3 + 5x)(x + -3)

Reorder the terms:
0 = (3 + 5x)(-3 + x)

Multiply (3 + 5x) * (-3 + x)
0 = (3(-3 + x) + 5x * (-3 + x))
0 = ((-3 * 3 + x * 3) + 5x * (-3 + x))
0 = ((-9 + 3x) + 5x * (-3 + x))
0 = (-9 + 3x + (-3 * 5x + x * 5x))
0 = (-9 + 3x + (-15x + 5x2))

Combine like terms: 3x + -15x = -12x
0 = (-9 + -12x + 5x2)

Solving
0 = -9 + -12x + 5x2

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(3 + -1x)(3 + 5x) = 0


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 '(3 + 5x)' equal to zero and attempt to solve:

Simplifying
3 + 5x = 0

Solving
3 + 5x = 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 + 5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5x = 0 + -3
5x = 0 + -3

Combine like terms: 0 + -3 = -3
5x = -3

Divide each side by '5'.
x = -0.6

Simplifying
x = -0.6
Solution
x = {3, -0.6}

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