(x-7)(2x+10)=0

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Solution for (x-7)(2x+10)=0 equation: 


Simplifying
(x + -7)(2x + 10) = 0

Reorder the terms:
(-7 + x)(2x + 10) = 0

Reorder the terms:
(-7 + x)(10 + 2x) = 0

Multiply (-7 + x) * (10 + 2x)
(-7(10 + 2x) + x(10 + 2x)) = 0
((10 * -7 + 2x * -7) + x(10 + 2x)) = 0
((-70 + -14x) + x(10 + 2x)) = 0
(-70 + -14x + (10 * x + 2x * x)) = 0
(-70 + -14x + (10x + 2x2)) = 0

Combine like terms: -14x + 10x = -4x
(-70 + -4x + 2x2) = 0

Solving
-70 + -4x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + -2x + x2) = 0

Factor a trinomial.
2((-5 + -1x)(7 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

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 = {-5, 7}

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