(x+4)(x+4)+(x-3)(x+4)=4

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Solution for (x+4)(x+4)+(x-3)(x+4)=4 equation:


Simplifying
(x + 4)(x + 4) + (x + -3)(x + 4) = 4

Reorder the terms:
(4 + x)(x + 4) + (x + -3)(x + 4) = 4

Reorder the terms:
(4 + x)(4 + x) + (x + -3)(x + 4) = 4

Multiply (4 + x) * (4 + x)
(4(4 + x) + x(4 + x)) + (x + -3)(x + 4) = 4
((4 * 4 + x * 4) + x(4 + x)) + (x + -3)(x + 4) = 4
((16 + 4x) + x(4 + x)) + (x + -3)(x + 4) = 4
(16 + 4x + (4 * x + x * x)) + (x + -3)(x + 4) = 4
(16 + 4x + (4x + x2)) + (x + -3)(x + 4) = 4

Combine like terms: 4x + 4x = 8x
(16 + 8x + x2) + (x + -3)(x + 4) = 4

Reorder the terms:
16 + 8x + x2 + (-3 + x)(x + 4) = 4

Reorder the terms:
16 + 8x + x2 + (-3 + x)(4 + x) = 4

Multiply (-3 + x) * (4 + x)
16 + 8x + x2 + (-3(4 + x) + x(4 + x)) = 4
16 + 8x + x2 + ((4 * -3 + x * -3) + x(4 + x)) = 4
16 + 8x + x2 + ((-12 + -3x) + x(4 + x)) = 4
16 + 8x + x2 + (-12 + -3x + (4 * x + x * x)) = 4
16 + 8x + x2 + (-12 + -3x + (4x + x2)) = 4

Combine like terms: -3x + 4x = 1x
16 + 8x + x2 + (-12 + 1x + x2) = 4

Reorder the terms:
16 + -12 + 8x + 1x + x2 + x2 = 4

Combine like terms: 16 + -12 = 4
4 + 8x + 1x + x2 + x2 = 4

Combine like terms: 8x + 1x = 9x
4 + 9x + x2 + x2 = 4

Combine like terms: x2 + x2 = 2x2
4 + 9x + 2x2 = 4

Add '-4' to each side of the equation.
4 + 9x + -4 + 2x2 = 4 + -4

Reorder the terms:
4 + -4 + 9x + 2x2 = 4 + -4

Combine like terms: 4 + -4 = 0
0 + 9x + 2x2 = 4 + -4
9x + 2x2 = 4 + -4

Combine like terms: 4 + -4 = 0
9x + 2x2 = 0

Solving
9x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(9 + 2x) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(9 + 2x)' equal to zero and attempt to solve: Simplifying 9 + 2x = 0 Solving 9 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2x = 0 + -9 2x = 0 + -9 Combine like terms: 0 + -9 = -9 2x = -9 Divide each side by '2'. x = -4.5 Simplifying x = -4.5

Solution

x = {0, -4.5}

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