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Simplifying (2x + 1) * x = 105 Reorder the terms: (1 + 2x) * x = 105 Reorder the terms for easier multiplication: x(1 + 2x) = 105 (1 * x + 2x * x) = 105 (1x + 2x2) = 105 Solving 1x + 2x2 = 105 Solving for variable 'x'. Reorder the terms: -105 + 1x + 2x2 = 105 + -105 Combine like terms: 105 + -105 = 0 -105 + 1x + 2x2 = 0 Factor a trinomial. (-15 + -2x)(7 + -1x) = 0Subproblem 1
Set the factor '(-15 + -2x)' equal to zero and attempt to solve: Simplifying -15 + -2x = 0 Solving -15 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -2x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -2x = 0 + 15 -2x = 0 + 15 Combine like terms: 0 + 15 = 15 -2x = 15 Divide each side by '-2'. x = -7.5 Simplifying x = -7.5Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {-7.5, 7}
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