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

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


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

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

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

Multiply (2 + 5x) * (5 + -4x)
0 = (2(5 + -4x) + 5x * (5 + -4x))
0 = ((5 * 2 + -4x * 2) + 5x * (5 + -4x))
0 = ((10 + -8x) + 5x * (5 + -4x))
0 = (10 + -8x + (5 * 5x + -4x * 5x))
0 = (10 + -8x + (25x + -20x2))

Combine like terms: -8x + 25x = 17x
0 = (10 + 17x + -20x2)

Solving
0 = 10 + 17x + -20x2

Solving for variable 'x'.

Combine like terms: 0 + -10 = -10
-10 + -17x + 20x2 = 10 + 17x + -20x2 + -10 + -17x + 20x2

Reorder the terms:
-10 + -17x + 20x2 = 10 + -10 + 17x + -17x + -20x2 + 20x2

Combine like terms: 10 + -10 = 0
-10 + -17x + 20x2 = 0 + 17x + -17x + -20x2 + 20x2
-10 + -17x + 20x2 = 17x + -17x + -20x2 + 20x2

Combine like terms: 17x + -17x = 0
-10 + -17x + 20x2 = 0 + -20x2 + 20x2
-10 + -17x + 20x2 = -20x2 + 20x2

Combine like terms: -20x2 + 20x2 = 0
-10 + -17x + 20x2 = 0

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


Subproblem 1
Set the factor '(-2 + -5x)' equal to zero and attempt to solve:

Simplifying
-2 + -5x = 0

Solving
-2 + -5x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -5x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5x = 0 + 2
-5x = 0 + 2

Combine like terms: 0 + 2 = 2
-5x = 2

Divide each side by '-5'.
x = -0.4

Simplifying
x = -0.4

Subproblem 2
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
Solution
x = {-0.4, 1.25}

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