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Simplifying 10x2 + 4x + -6 = 15x2 + -14x + 3 Reorder the terms: -6 + 4x + 10x2 = 15x2 + -14x + 3 Reorder the terms: -6 + 4x + 10x2 = 3 + -14x + 15x2 Solving -6 + 4x + 10x2 = 3 + -14x + 15x2 Solving for variable 'x'. Reorder the terms: -6 + -3 + 4x + 14x + 10x2 + -15x2 = 3 + -14x + 15x2 + -3 + 14x + -15x2 Combine like terms: -6 + -3 = -9 -9 + 4x + 14x + 10x2 + -15x2 = 3 + -14x + 15x2 + -3 + 14x + -15x2 Combine like terms: 4x + 14x = 18x -9 + 18x + 10x2 + -15x2 = 3 + -14x + 15x2 + -3 + 14x + -15x2 Combine like terms: 10x2 + -15x2 = -5x2 -9 + 18x + -5x2 = 3 + -14x + 15x2 + -3 + 14x + -15x2 Reorder the terms: -9 + 18x + -5x2 = 3 + -3 + -14x + 14x + 15x2 + -15x2 Combine like terms: 3 + -3 = 0 -9 + 18x + -5x2 = 0 + -14x + 14x + 15x2 + -15x2 -9 + 18x + -5x2 = -14x + 14x + 15x2 + -15x2 Combine like terms: -14x + 14x = 0 -9 + 18x + -5x2 = 0 + 15x2 + -15x2 -9 + 18x + -5x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 -9 + 18x + -5x2 = 0 Factor a trinomial. (-3 + x)(3 + -5x) = 0Subproblem 1
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 = 3Subproblem 2
Set the factor '(3 + -5x)' equal to zero and attempt to solve: Simplifying 3 + -5x = 0 Solving 3 + -5x = 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 + -5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5x = 0 + -3 -5x = 0 + -3 Combine like terms: 0 + -3 = -3 -5x = -3 Divide each side by '-5'. x = 0.6 Simplifying x = 0.6Solution
x = {3, 0.6}
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