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Simplifying 5x(x + 3) + -3x + 4 = 7(x + 2) Reorder the terms: 5x(3 + x) + -3x + 4 = 7(x + 2) (3 * 5x + x * 5x) + -3x + 4 = 7(x + 2) (15x + 5x2) + -3x + 4 = 7(x + 2) Reorder the terms: 4 + 15x + -3x + 5x2 = 7(x + 2) Combine like terms: 15x + -3x = 12x 4 + 12x + 5x2 = 7(x + 2) Reorder the terms: 4 + 12x + 5x2 = 7(2 + x) 4 + 12x + 5x2 = (2 * 7 + x * 7) 4 + 12x + 5x2 = (14 + 7x) Solving 4 + 12x + 5x2 = 14 + 7x Solving for variable 'x'. Reorder the terms: 4 + -14 + 12x + -7x + 5x2 = 14 + 7x + -14 + -7x Combine like terms: 4 + -14 = -10 -10 + 12x + -7x + 5x2 = 14 + 7x + -14 + -7x Combine like terms: 12x + -7x = 5x -10 + 5x + 5x2 = 14 + 7x + -14 + -7x Reorder the terms: -10 + 5x + 5x2 = 14 + -14 + 7x + -7x Combine like terms: 14 + -14 = 0 -10 + 5x + 5x2 = 0 + 7x + -7x -10 + 5x + 5x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -10 + 5x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-2 + x + x2) = 0 Factor a trinomial. 5((-2 + -1x)(1 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 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 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-2, 1}
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