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Simplifying (4x + 1)(x + -3) = 5(x + -3) Reorder the terms: (1 + 4x)(x + -3) = 5(x + -3) Reorder the terms: (1 + 4x)(-3 + x) = 5(x + -3) Multiply (1 + 4x) * (-3 + x) (1(-3 + x) + 4x * (-3 + x)) = 5(x + -3) ((-3 * 1 + x * 1) + 4x * (-3 + x)) = 5(x + -3) ((-3 + 1x) + 4x * (-3 + x)) = 5(x + -3) (-3 + 1x + (-3 * 4x + x * 4x)) = 5(x + -3) (-3 + 1x + (-12x + 4x2)) = 5(x + -3) Combine like terms: 1x + -12x = -11x (-3 + -11x + 4x2) = 5(x + -3) Reorder the terms: -3 + -11x + 4x2 = 5(-3 + x) -3 + -11x + 4x2 = (-3 * 5 + x * 5) -3 + -11x + 4x2 = (-15 + 5x) Solving -3 + -11x + 4x2 = -15 + 5x Solving for variable 'x'. Reorder the terms: -3 + 15 + -11x + -5x + 4x2 = -15 + 5x + 15 + -5x Combine like terms: -3 + 15 = 12 12 + -11x + -5x + 4x2 = -15 + 5x + 15 + -5x Combine like terms: -11x + -5x = -16x 12 + -16x + 4x2 = -15 + 5x + 15 + -5x Reorder the terms: 12 + -16x + 4x2 = -15 + 15 + 5x + -5x Combine like terms: -15 + 15 = 0 12 + -16x + 4x2 = 0 + 5x + -5x 12 + -16x + 4x2 = 5x + -5x Combine like terms: 5x + -5x = 0 12 + -16x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(3 + -4x + x2) = 0 Factor a trinomial. 4((1 + -1x)(3 + -1x)) = 0 Ignore the factor 4.Subproblem 1
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 = 1Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {1, 3}
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