(7-2x)*(2x-7)=-9

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Solution for (7-2x)*(2x-7)=-9 equation: 


Simplifying
(7 + -2x)(2x + -7) = -9

Reorder the terms:
(7 + -2x)(-7 + 2x) = -9

Multiply (7 + -2x) * (-7 + 2x)
(7(-7 + 2x) + -2x * (-7 + 2x)) = -9
((-7 * 7 + 2x * 7) + -2x * (-7 + 2x)) = -9
((-49 + 14x) + -2x * (-7 + 2x)) = -9
(-49 + 14x + (-7 * -2x + 2x * -2x)) = -9
(-49 + 14x + (14x + -4x2)) = -9

Combine like terms: 14x + 14x = 28x
(-49 + 28x + -4x2) = -9

Solving
-49 + 28x + -4x2 = -9

Solving for variable 'x'.

Reorder the terms:
-49 + 9 + 28x + -4x2 = -9 + 9

Combine like terms: -49 + 9 = -40
-40 + 28x + -4x2 = -9 + 9

Combine like terms: -9 + 9 = 0
-40 + 28x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-10 + 7x + -1x2) = 0

Factor a trinomial.
4((-5 + x)(2 + -1x)) = 0

Ignore the factor 4.

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

Simplifying
-5 + x = 0

Solving
-5 + x = 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 + x = 0 + 5

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

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

Simplifying
x = 5

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 = {5, 2}

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