(7-2x)(9-2x)=35

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Solution for (7-2x)(9-2x)=35 equation: 


Simplifying
(7 + -2x)(9 + -2x) = 35

Multiply (7 + -2x) * (9 + -2x)
(7(9 + -2x) + -2x * (9 + -2x)) = 35
((9 * 7 + -2x * 7) + -2x * (9 + -2x)) = 35
((63 + -14x) + -2x * (9 + -2x)) = 35
(63 + -14x + (9 * -2x + -2x * -2x)) = 35
(63 + -14x + (-18x + 4x2)) = 35

Combine like terms: -14x + -18x = -32x
(63 + -32x + 4x2) = 35

Solving
63 + -32x + 4x2 = 35

Solving for variable 'x'.

Reorder the terms:
63 + -35 + -32x + 4x2 = 35 + -35

Combine like terms: 63 + -35 = 28
28 + -32x + 4x2 = 35 + -35

Combine like terms: 35 + -35 = 0
28 + -32x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + -8x + x2) = 0

Factor a trinomial.
4((1 + -1x)(7 + -1x)) = 0

Ignore the factor 4.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

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 = {1, 7}

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