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Simplifying 3x(15 + -2x) = 84 (15 * 3x + -2x * 3x) = 84 (45x + -6x2) = 84 Solving 45x + -6x2 = 84 Solving for variable 'x'. Reorder the terms: -84 + 45x + -6x2 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + 45x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-28 + 15x + -2x2) = 0 Factor a trinomial. 3((-4 + x)(7 + -2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Simplifying x = 4Subproblem 2
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 = 3.5Solution
x = {4, 3.5}
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