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

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Solution for 5(x+10)(x-7)=0 equation: 


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

Reorder the terms:
5(10 + x)(x + -7) = 0

Reorder the terms:
5(10 + x)(-7 + x) = 0

Multiply (10 + x) * (-7 + x)
5(10(-7 + x) + x(-7 + x)) = 0
5((-7 * 10 + x * 10) + x(-7 + x)) = 0
5((-70 + 10x) + x(-7 + x)) = 0
5(-70 + 10x + (-7 * x + x * x)) = 0
5(-70 + 10x + (-7x + x2)) = 0

Combine like terms: 10x + -7x = 3x
5(-70 + 3x + x2) = 0
(-70 * 5 + 3x * 5 + x2 * 5) = 0
(-350 + 15x + 5x2) = 0

Solving
-350 + 15x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-70 + 3x + x2) = 0

Factor a trinomial.
5((-10 + -1x)(7 + -1x)) = 0

Ignore the factor 5.

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 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-10, 7}

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