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Simplifying (6x2 + 7x + -5) + -1(3x2 + 2x + -7) = 0 Reorder the terms: (-5 + 7x + 6x2) + -1(3x2 + 2x + -7) = 0 Remove parenthesis around (-5 + 7x + 6x2) -5 + 7x + 6x2 + -1(3x2 + 2x + -7) = 0 Reorder the terms: -5 + 7x + 6x2 + -1(-7 + 2x + 3x2) = 0 -5 + 7x + 6x2 + (-7 * -1 + 2x * -1 + 3x2 * -1) = 0 -5 + 7x + 6x2 + (7 + -2x + -3x2) = 0 Reorder the terms: -5 + 7 + 7x + -2x + 6x2 + -3x2 = 0 Combine like terms: -5 + 7 = 2 2 + 7x + -2x + 6x2 + -3x2 = 0 Combine like terms: 7x + -2x = 5x 2 + 5x + 6x2 + -3x2 = 0 Combine like terms: 6x2 + -3x2 = 3x2 2 + 5x + 3x2 = 0 Solving 2 + 5x + 3x2 = 0 Solving for variable 'x'. Factor a trinomial. (1 + x)(2 + 3x) = 0Subproblem 1
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 2
Set the factor '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667Solution
x = {-1, -0.6666666667}
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