(18-2x)(16-2x)=168

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Solution for (18-2x)(16-2x)=168 equation:


Simplifying
(18 + -2x)(16 + -2x) = 168

Multiply (18 + -2x) * (16 + -2x)
(18(16 + -2x) + -2x * (16 + -2x)) = 168
((16 * 18 + -2x * 18) + -2x * (16 + -2x)) = 168
((288 + -36x) + -2x * (16 + -2x)) = 168
(288 + -36x + (16 * -2x + -2x * -2x)) = 168
(288 + -36x + (-32x + 4x2)) = 168

Combine like terms: -36x + -32x = -68x
(288 + -68x + 4x2) = 168

Solving
288 + -68x + 4x2 = 168

Solving for variable 'x'.

Reorder the terms:
288 + -168 + -68x + 4x2 = 168 + -168

Combine like terms: 288 + -168 = 120
120 + -68x + 4x2 = 168 + -168

Combine like terms: 168 + -168 = 0
120 + -68x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(30 + -17x + x2) = 0

Factor a trinomial.
4((2 + -1x)(15 + -1x)) = 0

Ignore the factor 4.

Subproblem 1

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

Subproblem 2

Set the factor '(15 + -1x)' equal to zero and attempt to solve: Simplifying 15 + -1x = 0 Solving 15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1x = 0 + -15 -1x = 0 + -15 Combine like terms: 0 + -15 = -15 -1x = -15 Divide each side by '-1'. x = 15 Simplifying x = 15

Solution

x = {2, 15}

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