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Simplifying 4x2 + -90 = 5x2 + 21x Reorder the terms: -90 + 4x2 = 5x2 + 21x Reorder the terms: -90 + 4x2 = 21x + 5x2 Solving -90 + 4x2 = 21x + 5x2 Solving for variable 'x'. Reorder the terms: -90 + -21x + 4x2 + -5x2 = 21x + 5x2 + -21x + -5x2 Combine like terms: 4x2 + -5x2 = -1x2 -90 + -21x + -1x2 = 21x + 5x2 + -21x + -5x2 Reorder the terms: -90 + -21x + -1x2 = 21x + -21x + 5x2 + -5x2 Combine like terms: 21x + -21x = 0 -90 + -21x + -1x2 = 0 + 5x2 + -5x2 -90 + -21x + -1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -90 + -21x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(90 + 21x + x2) = 0 Factor a trinomial. -1((15 + x)(6 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + x)' equal to zero and attempt to solve: Simplifying 15 + x = 0 Solving 15 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + x = 0 + -15 x = 0 + -15 Combine like terms: 0 + -15 = -15 x = -15 Simplifying x = -15Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Solution
x = {-15, -6}
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