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

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


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

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

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

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

Combine like terms: -25x + 8x = -17x
5(-20 + -17x + 10x2) = 0
(-20 * 5 + -17x * 5 + 10x2 * 5) = 0
(-100 + -85x + 50x2) = 0

Solving
-100 + -85x + 50x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-20 + -17x + 10x2) = 0

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

Ignore the factor 5.

Subproblem 1
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

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 = {-0.8, 2.5}

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