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Simplifying 3x(2x + 7) = 45 Reorder the terms: 3x(7 + 2x) = 45 (7 * 3x + 2x * 3x) = 45 (21x + 6x2) = 45 Solving 21x + 6x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + 21x + 6x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + 21x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + 7x + 2x2) = 0 Factor a trinomial. 3((-5 + -1x)(3 + -2x)) = 0 Ignore the factor 3.Subproblem 1
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 = -5Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {-5, 1.5}
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