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

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


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

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

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

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

Combine like terms: -2x + 5x = 3x
4(-10 + 3x + x2) = 0
(-10 * 4 + 3x * 4 + x2 * 4) = 0
(-40 + 12x + 4x2) = 0

Solving
-40 + 12x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-10 + 3x + x2) = 0

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

Ignore the factor 4.

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

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-5, 2}

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