=(3x-8)(5x+6)

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Solution for =(3x-8)(5x+6) equation: 


Simplifying
0 = (3x + -8)(5x + 6)

Reorder the terms:
0 = (-8 + 3x)(5x + 6)

Reorder the terms:
0 = (-8 + 3x)(6 + 5x)

Multiply (-8 + 3x) * (6 + 5x)
0 = (-8(6 + 5x) + 3x * (6 + 5x))
0 = ((6 * -8 + 5x * -8) + 3x * (6 + 5x))
0 = ((-48 + -40x) + 3x * (6 + 5x))
0 = (-48 + -40x + (6 * 3x + 5x * 3x))
0 = (-48 + -40x + (18x + 15x2))

Combine like terms: -40x + 18x = -22x
0 = (-48 + -22x + 15x2)

Solving
0 = -48 + -22x + 15x2

Solving for variable 'x'.

Combine like terms: 0 + 48 = 48
48 + 22x + -15x2 = -48 + -22x + 15x2 + 48 + 22x + -15x2

Reorder the terms:
48 + 22x + -15x2 = -48 + 48 + -22x + 22x + 15x2 + -15x2

Combine like terms: -48 + 48 = 0
48 + 22x + -15x2 = 0 + -22x + 22x + 15x2 + -15x2
48 + 22x + -15x2 = -22x + 22x + 15x2 + -15x2

Combine like terms: -22x + 22x = 0
48 + 22x + -15x2 = 0 + 15x2 + -15x2
48 + 22x + -15x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
48 + 22x + -15x2 = 0

Factor a trinomial.
(8 + -3x)(6 + 5x) = 0


Subproblem 1
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667

Subproblem 2
Set the factor '(6 + 5x)' equal to zero and attempt to solve:

Simplifying
6 + 5x = 0

Solving
6 + 5x = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5x = 0 + -6
5x = 0 + -6

Combine like terms: 0 + -6 = -6
5x = -6

Divide each side by '5'.
x = -1.2

Simplifying
x = -1.2
Solution
x = {2.666666667, -1.2}

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