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Simplifying (x + -2) * 2 + x(x + -3) = 3(x + 4)(x + -3) + -1(x + 2)(x + -1) + 2 Reorder the terms: (-2 + x) * 2 + x(x + -3) = 3(x + 4)(x + -3) + -1(x + 2)(x + -1) + 2 Reorder the terms for easier multiplication: 2(-2 + x) + x(x + -3) = 3(x + 4)(x + -3) + -1(x + 2)(x + -1) + 2 (-2 * 2 + x * 2) + x(x + -3) = 3(x + 4)(x + -3) + -1(x + 2)(x + -1) + 2 (-4 + 2x) + x(x + -3) = 3(x + 4)(x + -3) + -1(x + 2)(x + -1) + 2 Reorder the terms: -4 + 2x + x(-3 + x) = 3(x + 4)(x + -3) + -1(x + 2)(x + -1) + 2 -4 + 2x + (-3 * x + x * x) = 3(x + 4)(x + -3) + -1(x + 2)(x + -1) + 2 -4 + 2x + (-3x + x2) = 3(x + 4)(x + -3) + -1(x + 2)(x + -1) + 2 Combine like terms: 2x + -3x = -1x -4 + -1x + x2 = 3(x + 4)(x + -3) + -1(x + 2)(x + -1) + 2 Reorder the terms: -4 + -1x + x2 = 3(4 + x)(x + -3) + -1(x + 2)(x + -1) + 2 Reorder the terms: -4 + -1x + x2 = 3(4 + x)(-3 + x) + -1(x + 2)(x + -1) + 2 Multiply (4 + x) * (-3 + x) -4 + -1x + x2 = 3(4(-3 + x) + x(-3 + x)) + -1(x + 2)(x + -1) + 2 -4 + -1x + x2 = 3((-3 * 4 + x * 4) + x(-3 + x)) + -1(x + 2)(x + -1) + 2 -4 + -1x + x2 = 3((-12 + 4x) + x(-3 + x)) + -1(x + 2)(x + -1) + 2 -4 + -1x + x2 = 3(-12 + 4x + (-3 * x + x * x)) + -1(x + 2)(x + -1) + 2 -4 + -1x + x2 = 3(-12 + 4x + (-3x + x2)) + -1(x + 2)(x + -1) + 2 Combine like terms: 4x + -3x = 1x -4 + -1x + x2 = 3(-12 + 1x + x2) + -1(x + 2)(x + -1) + 2 -4 + -1x + x2 = (-12 * 3 + 1x * 3 + x2 * 3) + -1(x + 2)(x + -1) + 2 -4 + -1x + x2 = (-36 + 3x + 3x2) + -1(x + 2)(x + -1) + 2 Reorder the terms: -4 + -1x + x2 = -36 + 3x + 3x2 + -1(2 + x)(x + -1) + 2 Reorder the terms: -4 + -1x + x2 = -36 + 3x + 3x2 + -1(2 + x)(-1 + x) + 2 Multiply (2 + x) * (-1 + x) -4 + -1x + x2 = -36 + 3x + 3x2 + -1(2(-1 + x) + x(-1 + x)) + 2 -4 + -1x + x2 = -36 + 3x + 3x2 + -1((-1 * 2 + x * 2) + x(-1 + x)) + 2 -4 + -1x + x2 = -36 + 3x + 3x2 + -1((-2 + 2x) + x(-1 + x)) + 2 -4 + -1x + x2 = -36 + 3x + 3x2 + -1(-2 + 2x + (-1 * x + x * x)) + 2 -4 + -1x + x2 = -36 + 3x + 3x2 + -1(-2 + 2x + (-1x + x2)) + 2 Combine like terms: 2x + -1x = 1x -4 + -1x + x2 = -36 + 3x + 3x2 + -1(-2 + 1x + x2) + 2 -4 + -1x + x2 = -36 + 3x + 3x2 + (-2 * -1 + 1x * -1 + x2 * -1) + 2 -4 + -1x + x2 = -36 + 3x + 3x2 + (2 + -1x + -1x2) + 2 Reorder the terms: -4 + -1x + x2 = -36 + 2 + 2 + 3x + -1x + 3x2 + -1x2 Combine like terms: -36 + 2 = -34 -4 + -1x + x2 = -34 + 2 + 3x + -1x + 3x2 + -1x2 Combine like terms: -34 + 2 = -32 -4 + -1x + x2 = -32 + 3x + -1x + 3x2 + -1x2 Combine like terms: 3x + -1x = 2x -4 + -1x + x2 = -32 + 2x + 3x2 + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -4 + -1x + x2 = -32 + 2x + 2x2 Solving -4 + -1x + x2 = -32 + 2x + 2x2 Solving for variable 'x'. Reorder the terms: -4 + 32 + -1x + -2x + x2 + -2x2 = -32 + 2x + 2x2 + 32 + -2x + -2x2 Combine like terms: -4 + 32 = 28 28 + -1x + -2x + x2 + -2x2 = -32 + 2x + 2x2 + 32 + -2x + -2x2 Combine like terms: -1x + -2x = -3x 28 + -3x + x2 + -2x2 = -32 + 2x + 2x2 + 32 + -2x + -2x2 Combine like terms: x2 + -2x2 = -1x2 28 + -3x + -1x2 = -32 + 2x + 2x2 + 32 + -2x + -2x2 Reorder the terms: 28 + -3x + -1x2 = -32 + 32 + 2x + -2x + 2x2 + -2x2 Combine like terms: -32 + 32 = 0 28 + -3x + -1x2 = 0 + 2x + -2x + 2x2 + -2x2 28 + -3x + -1x2 = 2x + -2x + 2x2 + -2x2 Combine like terms: 2x + -2x = 0 28 + -3x + -1x2 = 0 + 2x2 + -2x2 28 + -3x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 28 + -3x + -1x2 = 0 Factor a trinomial. (4 + -1x)(7 + x) = 0Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 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 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Solution
x = {4, -7}
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