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Simplifying 5x2 + 7x + 20 = 7x2 + 3x + -10 Reorder the terms: 20 + 7x + 5x2 = 7x2 + 3x + -10 Reorder the terms: 20 + 7x + 5x2 = -10 + 3x + 7x2 Solving 20 + 7x + 5x2 = -10 + 3x + 7x2 Solving for variable 'x'. Reorder the terms: 20 + 10 + 7x + -3x + 5x2 + -7x2 = -10 + 3x + 7x2 + 10 + -3x + -7x2 Combine like terms: 20 + 10 = 30 30 + 7x + -3x + 5x2 + -7x2 = -10 + 3x + 7x2 + 10 + -3x + -7x2 Combine like terms: 7x + -3x = 4x 30 + 4x + 5x2 + -7x2 = -10 + 3x + 7x2 + 10 + -3x + -7x2 Combine like terms: 5x2 + -7x2 = -2x2 30 + 4x + -2x2 = -10 + 3x + 7x2 + 10 + -3x + -7x2 Reorder the terms: 30 + 4x + -2x2 = -10 + 10 + 3x + -3x + 7x2 + -7x2 Combine like terms: -10 + 10 = 0 30 + 4x + -2x2 = 0 + 3x + -3x + 7x2 + -7x2 30 + 4x + -2x2 = 3x + -3x + 7x2 + -7x2 Combine like terms: 3x + -3x = 0 30 + 4x + -2x2 = 0 + 7x2 + -7x2 30 + 4x + -2x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 30 + 4x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 2x + -1x2) = 0 Factor a trinomial. 2((5 + -1x)(3 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {5, -3}
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