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Simplifying x(5x + 3) = 2x2 + -7x + 8 Reorder the terms: x(3 + 5x) = 2x2 + -7x + 8 (3 * x + 5x * x) = 2x2 + -7x + 8 (3x + 5x2) = 2x2 + -7x + 8 Reorder the terms: 3x + 5x2 = 8 + -7x + 2x2 Solving 3x + 5x2 = 8 + -7x + 2x2 Solving for variable 'x'. Reorder the terms: -8 + 3x + 7x + 5x2 + -2x2 = 8 + -7x + 2x2 + -8 + 7x + -2x2 Combine like terms: 3x + 7x = 10x -8 + 10x + 5x2 + -2x2 = 8 + -7x + 2x2 + -8 + 7x + -2x2 Combine like terms: 5x2 + -2x2 = 3x2 -8 + 10x + 3x2 = 8 + -7x + 2x2 + -8 + 7x + -2x2 Reorder the terms: -8 + 10x + 3x2 = 8 + -8 + -7x + 7x + 2x2 + -2x2 Combine like terms: 8 + -8 = 0 -8 + 10x + 3x2 = 0 + -7x + 7x + 2x2 + -2x2 -8 + 10x + 3x2 = -7x + 7x + 2x2 + -2x2 Combine like terms: -7x + 7x = 0 -8 + 10x + 3x2 = 0 + 2x2 + -2x2 -8 + 10x + 3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -8 + 10x + 3x2 = 0 Factor a trinomial. (-4 + -1x)(2 + -3x) = 0Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -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 = {-4, 0.6666666667}
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