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

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Solution for 0=(2x-3)(5x+4) equation: 


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

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

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

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

Combine like terms: -15x + 8x = -7x
0 = (-12 + -7x + 10x2)

Solving
0 = -12 + -7x + 10x2

Solving for variable 'x'.

Combine like terms: 0 + 12 = 12
12 + 7x + -10x2 = -12 + -7x + 10x2 + 12 + 7x + -10x2

Reorder the terms:
12 + 7x + -10x2 = -12 + 12 + -7x + 7x + 10x2 + -10x2

Combine like terms: -12 + 12 = 0
12 + 7x + -10x2 = 0 + -7x + 7x + 10x2 + -10x2
12 + 7x + -10x2 = -7x + 7x + 10x2 + -10x2

Combine like terms: -7x + 7x = 0
12 + 7x + -10x2 = 0 + 10x2 + -10x2
12 + 7x + -10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
12 + 7x + -10x2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(4 + 5x)' equal to zero and attempt to solve:

Simplifying
4 + 5x = 0

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

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

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

Divide each side by '5'.
x = -0.8

Simplifying
x = -0.8
Solution
x = {1.5, -0.8}

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