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Simplifying 4x2 + 6x = 7x2 + -12x Reorder the terms: 6x + 4x2 = 7x2 + -12x Reorder the terms: 6x + 4x2 = -12x + 7x2 Solving 6x + 4x2 = -12x + 7x2 Solving for variable 'x'. Reorder the terms: 6x + 12x + 4x2 + -7x2 = -12x + 7x2 + 12x + -7x2 Combine like terms: 6x + 12x = 18x 18x + 4x2 + -7x2 = -12x + 7x2 + 12x + -7x2 Combine like terms: 4x2 + -7x2 = -3x2 18x + -3x2 = -12x + 7x2 + 12x + -7x2 Reorder the terms: 18x + -3x2 = -12x + 12x + 7x2 + -7x2 Combine like terms: -12x + 12x = 0 18x + -3x2 = 0 + 7x2 + -7x2 18x + -3x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 18x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(6 + -1x) = 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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {0, 6}
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