(14-2x)(12-2x)=48

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Solution for (14-2x)(12-2x)=48 equation:


Simplifying
(14 + -2x)(12 + -2x) = 48

Multiply (14 + -2x) * (12 + -2x)
(14(12 + -2x) + -2x * (12 + -2x)) = 48
((12 * 14 + -2x * 14) + -2x * (12 + -2x)) = 48
((168 + -28x) + -2x * (12 + -2x)) = 48
(168 + -28x + (12 * -2x + -2x * -2x)) = 48
(168 + -28x + (-24x + 4x2)) = 48

Combine like terms: -28x + -24x = -52x
(168 + -52x + 4x2) = 48

Solving
168 + -52x + 4x2 = 48

Solving for variable 'x'.

Reorder the terms:
168 + -48 + -52x + 4x2 = 48 + -48

Combine like terms: 168 + -48 = 120
120 + -52x + 4x2 = 48 + -48

Combine like terms: 48 + -48 = 0
120 + -52x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(30 + -13x + x2) = 0

Factor a trinomial.
4((3 + -1x)(10 + -1x)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Subproblem 2

Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10

Solution

x = {3, 10}

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