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

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


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

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

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

Multiply (3 + 2x) * (-5 + 4x)
0 = (3(-5 + 4x) + 2x * (-5 + 4x))
0 = ((-5 * 3 + 4x * 3) + 2x * (-5 + 4x))
0 = ((-15 + 12x) + 2x * (-5 + 4x))
0 = (-15 + 12x + (-5 * 2x + 4x * 2x))
0 = (-15 + 12x + (-10x + 8x2))

Combine like terms: 12x + -10x = 2x
0 = (-15 + 2x + 8x2)

Solving
0 = -15 + 2x + 8x2

Solving for variable 'x'.

Combine like terms: 0 + 15 = 15
15 + -2x + -8x2 = -15 + 2x + 8x2 + 15 + -2x + -8x2

Reorder the terms:
15 + -2x + -8x2 = -15 + 15 + 2x + -2x + 8x2 + -8x2

Combine like terms: -15 + 15 = 0
15 + -2x + -8x2 = 0 + 2x + -2x + 8x2 + -8x2
15 + -2x + -8x2 = 2x + -2x + 8x2 + -8x2

Combine like terms: 2x + -2x = 0
15 + -2x + -8x2 = 0 + 8x2 + -8x2
15 + -2x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
15 + -2x + -8x2 = 0

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


Subproblem 1
Set the factor '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25

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

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {1.25, -1.5}

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