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Simplifying 3x2 + 8x + -10 = x2 + 7x + 5 Reorder the terms: -10 + 8x + 3x2 = x2 + 7x + 5 Reorder the terms: -10 + 8x + 3x2 = 5 + 7x + x2 Solving -10 + 8x + 3x2 = 5 + 7x + x2 Solving for variable 'x'. Reorder the terms: -10 + -5 + 8x + -7x + 3x2 + -1x2 = 5 + 7x + x2 + -5 + -7x + -1x2 Combine like terms: -10 + -5 = -15 -15 + 8x + -7x + 3x2 + -1x2 = 5 + 7x + x2 + -5 + -7x + -1x2 Combine like terms: 8x + -7x = 1x -15 + 1x + 3x2 + -1x2 = 5 + 7x + x2 + -5 + -7x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -15 + 1x + 2x2 = 5 + 7x + x2 + -5 + -7x + -1x2 Reorder the terms: -15 + 1x + 2x2 = 5 + -5 + 7x + -7x + x2 + -1x2 Combine like terms: 5 + -5 = 0 -15 + 1x + 2x2 = 0 + 7x + -7x + x2 + -1x2 -15 + 1x + 2x2 = 7x + -7x + x2 + -1x2 Combine like terms: 7x + -7x = 0 -15 + 1x + 2x2 = 0 + x2 + -1x2 -15 + 1x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -15 + 1x + 2x2 = 0 Factor a trinomial. (-3 + -1x)(5 + -2x) = 0Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 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 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {-3, 2.5}
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