0=(5x-2)(x+7)

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Solution for 0=(5x-2)(x+7) equation: 


Simplifying
0 = (5x + -2)(x + 7)

Reorder the terms:
0 = (-2 + 5x)(x + 7)

Reorder the terms:
0 = (-2 + 5x)(7 + x)

Multiply (-2 + 5x) * (7 + x)
0 = (-2(7 + x) + 5x * (7 + x))
0 = ((7 * -2 + x * -2) + 5x * (7 + x))
0 = ((-14 + -2x) + 5x * (7 + x))
0 = (-14 + -2x + (7 * 5x + x * 5x))
0 = (-14 + -2x + (35x + 5x2))

Combine like terms: -2x + 35x = 33x
0 = (-14 + 33x + 5x2)

Solving
0 = -14 + 33x + 5x2

Solving for variable 'x'.

Combine like terms: 0 + 14 = 14
14 + -33x + -5x2 = -14 + 33x + 5x2 + 14 + -33x + -5x2

Reorder the terms:
14 + -33x + -5x2 = -14 + 14 + 33x + -33x + 5x2 + -5x2

Combine like terms: -14 + 14 = 0
14 + -33x + -5x2 = 0 + 33x + -33x + 5x2 + -5x2
14 + -33x + -5x2 = 33x + -33x + 5x2 + -5x2

Combine like terms: 33x + -33x = 0
14 + -33x + -5x2 = 0 + 5x2 + -5x2
14 + -33x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
14 + -33x + -5x2 = 0

Factor a trinomial.
(2 + -5x)(7 + x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Solution
x = {0.4, -7}

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