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

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


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

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

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

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

Combine like terms: -25x + 8x = -17x
4(-10 + -17x + 20x2) = 0
(-10 * 4 + -17x * 4 + 20x2 * 4) = 0
(-40 + -68x + 80x2) = 0

Solving
-40 + -68x + 80x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-10 + -17x + 20x2) = 0

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

Ignore the factor 4.

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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