(5x-10)(3x+7)=0

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Solution for (5x-10)(3x+7)=0 equation: 


Simplifying
(5x + -10)(3x + 7) = 0

Reorder the terms:
(-10 + 5x)(3x + 7) = 0

Reorder the terms:
(-10 + 5x)(7 + 3x) = 0

Multiply (-10 + 5x) * (7 + 3x)
(-10(7 + 3x) + 5x * (7 + 3x)) = 0
((7 * -10 + 3x * -10) + 5x * (7 + 3x)) = 0
((-70 + -30x) + 5x * (7 + 3x)) = 0
(-70 + -30x + (7 * 5x + 3x * 5x)) = 0
(-70 + -30x + (35x + 15x2)) = 0

Combine like terms: -30x + 35x = 5x
(-70 + 5x + 15x2) = 0

Solving
-70 + 5x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-14 + x + 3x2) = 0

Factor a trinomial.
5((-7 + -3x)(2 + -1x)) = 0

Ignore the factor 5.

Subproblem 1
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

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-2.333333333, 2}

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