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Simplifying 3(18)(15) = (18 + x)(15 + x) Multiply 3 * 18 54 * 15 = (18 + x)(15 + x) Multiply 54 * 15 810 = (18 + x)(15 + x) Multiply (18 + x) * (15 + x) 810 = (18(15 + x) + x(15 + x)) 810 = ((15 * 18 + x * 18) + x(15 + x)) 810 = ((270 + 18x) + x(15 + x)) 810 = (270 + 18x + (15 * x + x * x)) 810 = (270 + 18x + (15x + x2)) Combine like terms: 18x + 15x = 33x 810 = (270 + 33x + x2) Solving 810 = 270 + 33x + x2 Solving for variable 'x'. Combine like terms: 810 + -270 = 540 540 + -33x + -1x2 = 270 + 33x + x2 + -270 + -33x + -1x2 Reorder the terms: 540 + -33x + -1x2 = 270 + -270 + 33x + -33x + x2 + -1x2 Combine like terms: 270 + -270 = 0 540 + -33x + -1x2 = 0 + 33x + -33x + x2 + -1x2 540 + -33x + -1x2 = 33x + -33x + x2 + -1x2 Combine like terms: 33x + -33x = 0 540 + -33x + -1x2 = 0 + x2 + -1x2 540 + -33x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 540 + -33x + -1x2 = 0 Factor a trinomial. (12 + -1x)(45 + x) = 0Subproblem 1
Set the factor '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Divide each side by '-1'. x = 12 Simplifying x = 12Subproblem 2
Set the factor '(45 + x)' equal to zero and attempt to solve: Simplifying 45 + x = 0 Solving 45 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + x = 0 + -45 Combine like terms: 45 + -45 = 0 0 + x = 0 + -45 x = 0 + -45 Combine like terms: 0 + -45 = -45 x = -45 Simplifying x = -45Solution
x = {12, -45}
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