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Simplifying 3x2 + -21x + 21 = x2 + -4x Reorder the terms: 21 + -21x + 3x2 = x2 + -4x Reorder the terms: 21 + -21x + 3x2 = -4x + x2 Solving 21 + -21x + 3x2 = -4x + x2 Solving for variable 'x'. Reorder the terms: 21 + -21x + 4x + 3x2 + -1x2 = -4x + x2 + 4x + -1x2 Combine like terms: -21x + 4x = -17x 21 + -17x + 3x2 + -1x2 = -4x + x2 + 4x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 21 + -17x + 2x2 = -4x + x2 + 4x + -1x2 Reorder the terms: 21 + -17x + 2x2 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 21 + -17x + 2x2 = 0 + x2 + -1x2 21 + -17x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 21 + -17x + 2x2 = 0 Factor a trinomial. (3 + -2x)(7 + -1x) = 0Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {1.5, 7}
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