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

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


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

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

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

Multiply (-7 + 3x) * (10 + x)
(-7(10 + x) + 3x * (10 + x)) = 0
((10 * -7 + x * -7) + 3x * (10 + x)) = 0
((-70 + -7x) + 3x * (10 + x)) = 0
(-70 + -7x + (10 * 3x + x * 3x)) = 0
(-70 + -7x + (30x + 3x2)) = 0

Combine like terms: -7x + 30x = 23x
(-70 + 23x + 3x2) = 0

Solving
-70 + 23x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-10 + -1x)(7 + -3x) = 0


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

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 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 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10

Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {-10, 2.333333333}

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