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Simplifying 300x = 10x2 + 30x + 120x + 360 Reorder the terms: 300x = 360 + 30x + 120x + 10x2 Combine like terms: 30x + 120x = 150x 300x = 360 + 150x + 10x2 Solving 300x = 360 + 150x + 10x2 Solving for variable 'x'. Reorder the terms: -360 + 300x + -150x + -10x2 = 360 + 150x + 10x2 + -360 + -150x + -10x2 Combine like terms: 300x + -150x = 150x -360 + 150x + -10x2 = 360 + 150x + 10x2 + -360 + -150x + -10x2 Reorder the terms: -360 + 150x + -10x2 = 360 + -360 + 150x + -150x + 10x2 + -10x2 Combine like terms: 360 + -360 = 0 -360 + 150x + -10x2 = 0 + 150x + -150x + 10x2 + -10x2 -360 + 150x + -10x2 = 150x + -150x + 10x2 + -10x2 Combine like terms: 150x + -150x = 0 -360 + 150x + -10x2 = 0 + 10x2 + -10x2 -360 + 150x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -360 + 150x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-36 + 15x + -1x2) = 0 Factor a trinomial. 10((-12 + x)(3 + -1x)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-12 + x)' equal to zero and attempt to solve: Simplifying -12 + x = 0 Solving -12 + x = 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 + x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + x = 0 + 12 x = 0 + 12 Combine like terms: 0 + 12 = 12 x = 12 Simplifying x = 12Subproblem 2
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 = 3Solution
x = {12, 3}
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