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Simplifying 5x2 + 32x + 20 = -10x2 + x + 6 Reorder the terms: 20 + 32x + 5x2 = -10x2 + x + 6 Reorder the terms: 20 + 32x + 5x2 = 6 + x + -10x2 Solving 20 + 32x + 5x2 = 6 + x + -10x2 Solving for variable 'x'. Reorder the terms: 20 + -6 + 32x + -1x + 5x2 + 10x2 = 6 + x + -10x2 + -6 + -1x + 10x2 Combine like terms: 20 + -6 = 14 14 + 32x + -1x + 5x2 + 10x2 = 6 + x + -10x2 + -6 + -1x + 10x2 Combine like terms: 32x + -1x = 31x 14 + 31x + 5x2 + 10x2 = 6 + x + -10x2 + -6 + -1x + 10x2 Combine like terms: 5x2 + 10x2 = 15x2 14 + 31x + 15x2 = 6 + x + -10x2 + -6 + -1x + 10x2 Reorder the terms: 14 + 31x + 15x2 = 6 + -6 + x + -1x + -10x2 + 10x2 Combine like terms: 6 + -6 = 0 14 + 31x + 15x2 = 0 + x + -1x + -10x2 + 10x2 14 + 31x + 15x2 = x + -1x + -10x2 + 10x2 Combine like terms: x + -1x = 0 14 + 31x + 15x2 = 0 + -10x2 + 10x2 14 + 31x + 15x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 14 + 31x + 15x2 = 0 Factor a trinomial. (7 + 5x)(2 + 3x) = 0Subproblem 1
Set the factor '(7 + 5x)' equal to zero and attempt to solve: Simplifying 7 + 5x = 0 Solving 7 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 5x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5x = 0 + -7 5x = 0 + -7 Combine like terms: 0 + -7 = -7 5x = -7 Divide each side by '5'. x = -1.4 Simplifying x = -1.4Subproblem 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 = {-1.4, -0.6666666667}
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