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Simplifying [2(x + -1)(x + -1)] + [3(x + -1)] + [3(x + -1)] + 4 = 420 Reorder the terms: [2(-1 + x)(x + -1)] + [3(x + -1)] + [3(x + -1)] + 4 = 420 Reorder the terms: [2(-1 + x)(-1 + x)] + [3(x + -1)] + [3(x + -1)] + 4 = 420 Multiply (-1 + x) * (-1 + x) [2(-1(-1 + x) + x(-1 + x))] + [3(x + -1)] + [3(x + -1)] + 4 = 420 [2((-1 * -1 + x * -1) + x(-1 + x))] + [3(x + -1)] + [3(x + -1)] + 4 = 420 [2((1 + -1x) + x(-1 + x))] + [3(x + -1)] + [3(x + -1)] + 4 = 420 [2(1 + -1x + (-1 * x + x * x))] + [3(x + -1)] + [3(x + -1)] + 4 = 420 [2(1 + -1x + (-1x + x2))] + [3(x + -1)] + [3(x + -1)] + 4 = 420 Combine like terms: -1x + -1x = -2x [2(1 + -2x + x2)] + [3(x + -1)] + [3(x + -1)] + 4 = 420 [(1 * 2 + -2x * 2 + x2 * 2)] + [3(x + -1)] + [3(x + -1)] + 4 = 420 [(2 + -4x + 2x2)] + [3(x + -1)] + [3(x + -1)] + 4 = 420 [2 + -4x + 2x2] + [3(x + -1)] + [3(x + -1)] + 4 = 420 Remove brackets around [2 + -4x + 2x2] 2 + -4x + 2x2 + [3(x + -1)] + [3(x + -1)] + 4 = 420 Reorder the terms: 2 + -4x + 2x2 + [3(-1 + x)] + [3(x + -1)] + 4 = 420 2 + -4x + 2x2 + [(-1 * 3 + x * 3)] + [3(x + -1)] + 4 = 420 2 + -4x + 2x2 + [(-3 + 3x)] + [3(x + -1)] + 4 = 420 2 + -4x + 2x2 + [-3 + 3x] + [3(x + -1)] + 4 = 420 Remove brackets around [-3 + 3x] 2 + -4x + 2x2 + -3 + 3x + [3(x + -1)] + 4 = 420 Reorder the terms: 2 + -4x + 2x2 + -3 + 3x + [3(-1 + x)] + 4 = 420 2 + -4x + 2x2 + -3 + 3x + [(-1 * 3 + x * 3)] + 4 = 420 2 + -4x + 2x2 + -3 + 3x + [(-3 + 3x)] + 4 = 420 2 + -4x + 2x2 + -3 + 3x + [-3 + 3x] + 4 = 420 Remove brackets around [-3 + 3x] 2 + -4x + 2x2 + -3 + 3x + -3 + 3x + 4 = 420 Reorder the terms: 2 + -3 + -3 + 4 + -4x + 3x + 3x + 2x2 = 420 Combine like terms: 2 + -3 = -1 -1 + -3 + 4 + -4x + 3x + 3x + 2x2 = 420 Combine like terms: -1 + -3 = -4 -4 + 4 + -4x + 3x + 3x + 2x2 = 420 Combine like terms: -4 + 4 = 0 0 + -4x + 3x + 3x + 2x2 = 420 -4x + 3x + 3x + 2x2 = 420 Combine like terms: -4x + 3x = -1x -1x + 3x + 2x2 = 420 Combine like terms: -1x + 3x = 2x 2x + 2x2 = 420 Solving 2x + 2x2 = 420 Solving for variable 'x'. Reorder the terms: -420 + 2x + 2x2 = 420 + -420 Combine like terms: 420 + -420 = 0 -420 + 2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-210 + x + x2) = 0 Factor a trinomial. 2((-15 + -1x)(14 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve: Simplifying -15 + -1x = 0 Solving -15 + -1x = 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 + -1x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1x = 0 + 15 -1x = 0 + 15 Combine like terms: 0 + 15 = 15 -1x = 15 Divide each side by '-1'. x = -15 Simplifying x = -15Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve: Simplifying 14 + -1x = 0 Solving 14 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1x = 0 + -14 -1x = 0 + -14 Combine like terms: 0 + -14 = -14 -1x = -14 Divide each side by '-1'. x = 14 Simplifying x = 14Solution
x = {-15, 14}
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