=(3x-4)(2x+5)

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Solution for =(3x-4)(2x+5) equation: 


Simplifying
0 = (3x + -4)(2x + 5)

Reorder the terms:
0 = (-4 + 3x)(2x + 5)

Reorder the terms:
0 = (-4 + 3x)(5 + 2x)

Multiply (-4 + 3x) * (5 + 2x)
0 = (-4(5 + 2x) + 3x * (5 + 2x))
0 = ((5 * -4 + 2x * -4) + 3x * (5 + 2x))
0 = ((-20 + -8x) + 3x * (5 + 2x))
0 = (-20 + -8x + (5 * 3x + 2x * 3x))
0 = (-20 + -8x + (15x + 6x2))

Combine like terms: -8x + 15x = 7x
0 = (-20 + 7x + 6x2)

Solving
0 = -20 + 7x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + 20 = 20
20 + -7x + -6x2 = -20 + 7x + 6x2 + 20 + -7x + -6x2

Reorder the terms:
20 + -7x + -6x2 = -20 + 20 + 7x + -7x + 6x2 + -6x2

Combine like terms: -20 + 20 = 0
20 + -7x + -6x2 = 0 + 7x + -7x + 6x2 + -6x2
20 + -7x + -6x2 = 7x + -7x + 6x2 + -6x2

Combine like terms: 7x + -7x = 0
20 + -7x + -6x2 = 0 + 6x2 + -6x2
20 + -7x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
20 + -7x + -6x2 = 0

Factor a trinomial.
(4 + -3x)(5 + 2x) = 0


Subproblem 1
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

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

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

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333

Subproblem 2
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
Solution
x = {1.333333333, -2.5}

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