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

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


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

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

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

Multiply (-2 + 7x) * (7 + 2x)
(-2(7 + 2x) + 7x * (7 + 2x)) = 0
((7 * -2 + 2x * -2) + 7x * (7 + 2x)) = 0
((-14 + -4x) + 7x * (7 + 2x)) = 0
(-14 + -4x + (7 * 7x + 2x * 7x)) = 0
(-14 + -4x + (49x + 14x2)) = 0

Combine like terms: -4x + 49x = 45x
(-14 + 45x + 14x2) = 0

Solving
-14 + 45x + 14x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 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 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

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

Simplifying
2 + -7x = 0

Solving
2 + -7x = 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 + -7x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7x = 0 + -2
-7x = 0 + -2

Combine like terms: 0 + -2 = -2
-7x = -2

Divide each side by '-7'.
x = 0.2857142857

Simplifying
x = 0.2857142857
Solution
x = {-3.5, 0.2857142857}

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