(x+2)(4x-10)=0

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Solution for (x+2)(4x-10)=0 equation: 


Simplifying
(x + 2)(4x + -10) = 0

Reorder the terms:
(2 + x)(4x + -10) = 0

Reorder the terms:
(2 + x)(-10 + 4x) = 0

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

Combine like terms: 8x + -10x = -2x
(-20 + -2x + 4x2) = 0

Solving
-20 + -2x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -1x + 2x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

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 = {-2, 2.5}

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