=(8+x)(5x+2)

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Solution for =(8+x)(5x+2) equation: 


Simplifying
0 = (8 + x)(5x + 2)

Reorder the terms:
0 = (8 + x)(2 + 5x)

Multiply (8 + x) * (2 + 5x)
0 = (8(2 + 5x) + x(2 + 5x))
0 = ((2 * 8 + 5x * 8) + x(2 + 5x))
0 = ((16 + 40x) + x(2 + 5x))
0 = (16 + 40x + (2 * x + 5x * x))
0 = (16 + 40x + (2x + 5x2))

Combine like terms: 40x + 2x = 42x
0 = (16 + 42x + 5x2)

Solving
0 = 16 + 42x + 5x2

Solving for variable 'x'.

Combine like terms: 0 + -16 = -16
-16 + -42x + -5x2 = 16 + 42x + 5x2 + -16 + -42x + -5x2

Reorder the terms:
-16 + -42x + -5x2 = 16 + -16 + 42x + -42x + 5x2 + -5x2

Combine like terms: 16 + -16 = 0
-16 + -42x + -5x2 = 0 + 42x + -42x + 5x2 + -5x2
-16 + -42x + -5x2 = 42x + -42x + 5x2 + -5x2

Combine like terms: 42x + -42x = 0
-16 + -42x + -5x2 = 0 + 5x2 + -5x2
-16 + -42x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-16 + -42x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(16 + 42x + 5x2) = 0

Factor a trinomial.
-1((8 + x)(2 + 5x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8

Subproblem 2
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
Solution
x = {-8, -0.4}

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