7x+151=(2x+29)(2x+29)

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Solution for 7x+151=(2x+29)(2x+29) equation: 


Simplifying
7x + 151 = (2x + 29)(2x + 29)

Reorder the terms:
151 + 7x = (2x + 29)(2x + 29)

Reorder the terms:
151 + 7x = (29 + 2x)(2x + 29)

Reorder the terms:
151 + 7x = (29 + 2x)(29 + 2x)

Multiply (29 + 2x) * (29 + 2x)
151 + 7x = (29(29 + 2x) + 2x * (29 + 2x))
151 + 7x = ((29 * 29 + 2x * 29) + 2x * (29 + 2x))
151 + 7x = ((841 + 58x) + 2x * (29 + 2x))
151 + 7x = (841 + 58x + (29 * 2x + 2x * 2x))
151 + 7x = (841 + 58x + (58x + 4x2))

Combine like terms: 58x + 58x = 116x
151 + 7x = (841 + 116x + 4x2)

Solving
151 + 7x = 841 + 116x + 4x2

Solving for variable 'x'.

Reorder the terms:
151 + -841 + 7x + -116x + -4x2 = 841 + 116x + 4x2 + -841 + -116x + -4x2

Combine like terms: 151 + -841 = -690
-690 + 7x + -116x + -4x2 = 841 + 116x + 4x2 + -841 + -116x + -4x2

Combine like terms: 7x + -116x = -109x
-690 + -109x + -4x2 = 841 + 116x + 4x2 + -841 + -116x + -4x2

Reorder the terms:
-690 + -109x + -4x2 = 841 + -841 + 116x + -116x + 4x2 + -4x2

Combine like terms: 841 + -841 = 0
-690 + -109x + -4x2 = 0 + 116x + -116x + 4x2 + -4x2
-690 + -109x + -4x2 = 116x + -116x + 4x2 + -4x2

Combine like terms: 116x + -116x = 0
-690 + -109x + -4x2 = 0 + 4x2 + -4x2
-690 + -109x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-690 + -109x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(690 + 109x + 4x2) = 0

Factor a trinomial.
-1((69 + 4x)(10 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(69 + 4x)' equal to zero and attempt to solve:

Simplifying
69 + 4x = 0

Solving
69 + 4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-69' to each side of the equation.
69 + -69 + 4x = 0 + -69

Combine like terms: 69 + -69 = 0
0 + 4x = 0 + -69
4x = 0 + -69

Combine like terms: 0 + -69 = -69
4x = -69

Divide each side by '4'.
x = -17.25

Simplifying
x = -17.25

Subproblem 2
Set the factor '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10
Solution
x = {-17.25, -10}

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