=(3x-5)(4x+3)

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Solution for =(3x-5)(4x+3) equation: 


Simplifying
0 = (3x + -5)(4x + 3)

Reorder the terms:
0 = (-5 + 3x)(4x + 3)

Reorder the terms:
0 = (-5 + 3x)(3 + 4x)

Multiply (-5 + 3x) * (3 + 4x)
0 = (-5(3 + 4x) + 3x * (3 + 4x))
0 = ((3 * -5 + 4x * -5) + 3x * (3 + 4x))
0 = ((-15 + -20x) + 3x * (3 + 4x))
0 = (-15 + -20x + (3 * 3x + 4x * 3x))
0 = (-15 + -20x + (9x + 12x2))

Combine like terms: -20x + 9x = -11x
0 = (-15 + -11x + 12x2)

Solving
0 = -15 + -11x + 12x2

Solving for variable 'x'.

Combine like terms: 0 + 15 = 15
15 + 11x + -12x2 = -15 + -11x + 12x2 + 15 + 11x + -12x2

Reorder the terms:
15 + 11x + -12x2 = -15 + 15 + -11x + 11x + 12x2 + -12x2

Combine like terms: -15 + 15 = 0
15 + 11x + -12x2 = 0 + -11x + 11x + 12x2 + -12x2
15 + 11x + -12x2 = -11x + 11x + 12x2 + -12x2

Combine like terms: -11x + 11x = 0
15 + 11x + -12x2 = 0 + 12x2 + -12x2
15 + 11x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
15 + 11x + -12x2 = 0

Factor a trinomial.
(5 + -3x)(3 + 4x) = 0


Subproblem 1
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

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

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

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

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667

Subproblem 2
Set the factor '(3 + 4x)' equal to zero and attempt to solve:

Simplifying
3 + 4x = 0

Solving
3 + 4x = 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 + 4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4x = 0 + -3
4x = 0 + -3

Combine like terms: 0 + -3 = -3
4x = -3

Divide each side by '4'.
x = -0.75

Simplifying
x = -0.75
Solution
x = {1.666666667, -0.75}

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