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

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


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

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

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

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

Combine like terms: -8x + 5x = -3x
0 = (-20 + -3x + 2x2)

Solving
0 = -20 + -3x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 20 = 20
20 + 3x + -2x2 = -20 + -3x + 2x2 + 20 + 3x + -2x2

Reorder the terms:
20 + 3x + -2x2 = -20 + 20 + -3x + 3x + 2x2 + -2x2

Combine like terms: -20 + 20 = 0
20 + 3x + -2x2 = 0 + -3x + 3x + 2x2 + -2x2
20 + 3x + -2x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
20 + 3x + -2x2 = 0 + 2x2 + -2x2
20 + 3x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
20 + 3x + -2x2 = 0

Factor a trinomial.
(4 + -1x)(5 + 2x) = 0


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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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 = {4, -2.5}

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