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Simplifying (19x2 + 12x + 12) = (7x2 + 10x + 12) Reorder the terms: (12 + 12x + 19x2) = (7x2 + 10x + 12) Remove parenthesis around (12 + 12x + 19x2) 12 + 12x + 19x2 = (7x2 + 10x + 12) Reorder the terms: 12 + 12x + 19x2 = (12 + 10x + 7x2) Remove parenthesis around (12 + 10x + 7x2) 12 + 12x + 19x2 = 12 + 10x + 7x2 Add '-12' to each side of the equation. 12 + 12x + -12 + 19x2 = 12 + 10x + -12 + 7x2 Reorder the terms: 12 + -12 + 12x + 19x2 = 12 + 10x + -12 + 7x2 Combine like terms: 12 + -12 = 0 0 + 12x + 19x2 = 12 + 10x + -12 + 7x2 12x + 19x2 = 12 + 10x + -12 + 7x2 Reorder the terms: 12x + 19x2 = 12 + -12 + 10x + 7x2 Combine like terms: 12 + -12 = 0 12x + 19x2 = 0 + 10x + 7x2 12x + 19x2 = 10x + 7x2 Solving 12x + 19x2 = 10x + 7x2 Solving for variable 'x'. Reorder the terms: 12x + -10x + 19x2 + -7x2 = 10x + 7x2 + -10x + -7x2 Combine like terms: 12x + -10x = 2x 2x + 19x2 + -7x2 = 10x + 7x2 + -10x + -7x2 Combine like terms: 19x2 + -7x2 = 12x2 2x + 12x2 = 10x + 7x2 + -10x + -7x2 Reorder the terms: 2x + 12x2 = 10x + -10x + 7x2 + -7x2 Combine like terms: 10x + -10x = 0 2x + 12x2 = 0 + 7x2 + -7x2 2x + 12x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 2x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(1 + 6x) = 0 Ignore the factor 2.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 '(1 + 6x)' equal to zero and attempt to solve: Simplifying 1 + 6x = 0 Solving 1 + 6x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 6x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6x = 0 + -1 6x = 0 + -1 Combine like terms: 0 + -1 = -1 6x = -1 Divide each side by '6'. x = -0.1666666667 Simplifying x = -0.1666666667Solution
x = {0, -0.1666666667}
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