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Simplifying 3x(2x + -3) = 105 Reorder the terms: 3x(-3 + 2x) = 105 (-3 * 3x + 2x * 3x) = 105 (-9x + 6x2) = 105 Solving -9x + 6x2 = 105 Solving for variable 'x'. Reorder the terms: -105 + -9x + 6x2 = 105 + -105 Combine like terms: 105 + -105 = 0 -105 + -9x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-35 + -3x + 2x2) = 0 Factor a trinomial. 3((-7 + -2x)(5 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve: Simplifying -7 + -2x = 0 Solving -7 + -2x = 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 + -2x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2x = 0 + 7 -2x = 0 + 7 Combine like terms: 0 + 7 = 7 -2x = 7 Divide each side by '-2'. x = -3.5 Simplifying x = -3.5Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-3.5, 5}
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