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

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


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

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

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

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

Combine like terms: -8x + -5x = -13x
5(20 + -13x + 2x2) = 0
(20 * 5 + -13x * 5 + 2x2 * 5) = 0
(100 + -65x + 10x2) = 0

Solving
100 + -65x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(20 + -13x + 2x2) = 0

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

Ignore the factor 5.

Subproblem 1
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

Subproblem 2
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
Solution
x = {2.5, 4}

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