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Simplifying 3x2 + 14x + 3 = -1 + 4(x + 1) Reorder the terms: 3 + 14x + 3x2 = -1 + 4(x + 1) Reorder the terms: 3 + 14x + 3x2 = -1 + 4(1 + x) 3 + 14x + 3x2 = -1 + (1 * 4 + x * 4) 3 + 14x + 3x2 = -1 + (4 + 4x) Combine like terms: -1 + 4 = 3 3 + 14x + 3x2 = 3 + 4x Add '-3' to each side of the equation. 3 + 14x + -3 + 3x2 = 3 + -3 + 4x Reorder the terms: 3 + -3 + 14x + 3x2 = 3 + -3 + 4x Combine like terms: 3 + -3 = 0 0 + 14x + 3x2 = 3 + -3 + 4x 14x + 3x2 = 3 + -3 + 4x Combine like terms: 3 + -3 = 0 14x + 3x2 = 0 + 4x 14x + 3x2 = 4x Solving 14x + 3x2 = 4x Solving for variable 'x'. Reorder the terms: 14x + -4x + 3x2 = 4x + -4x Combine like terms: 14x + -4x = 10x 10x + 3x2 = 4x + -4x Combine like terms: 4x + -4x = 0 10x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(10 + 3x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(10 + 3x)' equal to zero and attempt to solve: Simplifying 10 + 3x = 0 Solving 10 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + 3x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 3x = 0 + -10 3x = 0 + -10 Combine like terms: 0 + -10 = -10 3x = -10 Divide each side by '3'. x = -3.333333333 Simplifying x = -3.333333333Solution
x = {0, -3.333333333}
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