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Simplifying 4x2 + 14x = x2 + 23x Reorder the terms: 14x + 4x2 = x2 + 23x Reorder the terms: 14x + 4x2 = 23x + x2 Solving 14x + 4x2 = 23x + x2 Solving for variable 'x'. Reorder the terms: 14x + -23x + 4x2 + -1x2 = 23x + x2 + -23x + -1x2 Combine like terms: 14x + -23x = -9x -9x + 4x2 + -1x2 = 23x + x2 + -23x + -1x2 Combine like terms: 4x2 + -1x2 = 3x2 -9x + 3x2 = 23x + x2 + -23x + -1x2 Reorder the terms: -9x + 3x2 = 23x + -23x + x2 + -1x2 Combine like terms: 23x + -23x = 0 -9x + 3x2 = 0 + x2 + -1x2 -9x + 3x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -9x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(-3 + x) = 0 Ignore the factor 3.Subproblem 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 '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3Solution
x = {0, 3}
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