0=(3x-10)(x+7)

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Solution for 0=(3x-10)(x+7) equation: 


Simplifying
0 = (3x + -10)(x + 7)

Reorder the terms:
0 = (-10 + 3x)(x + 7)

Reorder the terms:
0 = (-10 + 3x)(7 + x)

Multiply (-10 + 3x) * (7 + x)
0 = (-10(7 + x) + 3x * (7 + x))
0 = ((7 * -10 + x * -10) + 3x * (7 + x))
0 = ((-70 + -10x) + 3x * (7 + x))
0 = (-70 + -10x + (7 * 3x + x * 3x))
0 = (-70 + -10x + (21x + 3x2))

Combine like terms: -10x + 21x = 11x
0 = (-70 + 11x + 3x2)

Solving
0 = -70 + 11x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 70 = 70
70 + -11x + -3x2 = -70 + 11x + 3x2 + 70 + -11x + -3x2

Reorder the terms:
70 + -11x + -3x2 = -70 + 70 + 11x + -11x + 3x2 + -3x2

Combine like terms: -70 + 70 = 0
70 + -11x + -3x2 = 0 + 11x + -11x + 3x2 + -3x2
70 + -11x + -3x2 = 11x + -11x + 3x2 + -3x2

Combine like terms: 11x + -11x = 0
70 + -11x + -3x2 = 0 + 3x2 + -3x2
70 + -11x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
70 + -11x + -3x2 = 0

Factor a trinomial.
(10 + -3x)(7 + x) = 0


Subproblem 1
Set the factor '(10 + -3x)' equal to zero and attempt to solve:

Simplifying
10 + -3x = 0

Solving
10 + -3x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3x = 0 + -10
-3x = 0 + -10

Combine like terms: 0 + -10 = -10
-3x = -10

Divide each side by '-3'.
x = 3.333333333

Simplifying
x = 3.333333333

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 = {3.333333333, -7}

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