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Simplifying 4x2 + -3x + 6 = -7x2 + 3x + 6 Reorder the terms: 6 + -3x + 4x2 = -7x2 + 3x + 6 Reorder the terms: 6 + -3x + 4x2 = 6 + 3x + -7x2 Add '-6' to each side of the equation. 6 + -3x + -6 + 4x2 = 6 + 3x + -6 + -7x2 Reorder the terms: 6 + -6 + -3x + 4x2 = 6 + 3x + -6 + -7x2 Combine like terms: 6 + -6 = 0 0 + -3x + 4x2 = 6 + 3x + -6 + -7x2 -3x + 4x2 = 6 + 3x + -6 + -7x2 Reorder the terms: -3x + 4x2 = 6 + -6 + 3x + -7x2 Combine like terms: 6 + -6 = 0 -3x + 4x2 = 0 + 3x + -7x2 -3x + 4x2 = 3x + -7x2 Solving -3x + 4x2 = 3x + -7x2 Solving for variable 'x'. Reorder the terms: -3x + -3x + 4x2 + 7x2 = 3x + -7x2 + -3x + 7x2 Combine like terms: -3x + -3x = -6x -6x + 4x2 + 7x2 = 3x + -7x2 + -3x + 7x2 Combine like terms: 4x2 + 7x2 = 11x2 -6x + 11x2 = 3x + -7x2 + -3x + 7x2 Reorder the terms: -6x + 11x2 = 3x + -3x + -7x2 + 7x2 Combine like terms: 3x + -3x = 0 -6x + 11x2 = 0 + -7x2 + 7x2 -6x + 11x2 = -7x2 + 7x2 Combine like terms: -7x2 + 7x2 = 0 -6x + 11x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + 11x) = 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 '(-6 + 11x)' equal to zero and attempt to solve: Simplifying -6 + 11x = 0 Solving -6 + 11x = 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 + 11x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 11x = 0 + 6 11x = 0 + 6 Combine like terms: 0 + 6 = 6 11x = 6 Divide each side by '11'. x = 0.5454545455 Simplifying x = 0.5454545455Solution
x = {0, 0.5454545455}
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